Are you going to have the AC jack (power entry module) on your new back plate? If so, what kind of terminals does it have on the inner side? A photo or a pencil sketch of your new back plate could help us visualize the problem.
Without knowing anything else, I would recommend splicing the wires with a crimped butt terminal (like this one or this one). It's a thin-wall metal tube inside of an insulating plastic tube. Each end of the tube can be crimped onto a wire. Here in the US, you can get them in any hardware store. Crimped connections are less brittle, compared to soldering.
Splicing plus soldering works too. Heat shrink is a more reliable insulation than tape.
Look for a FAQ or pinout information online that pertains to the specific series of battery / laptop that is to be involved. The pinout and charging requirements vary significantly depending on the particular series of battery and laptop involved.
In general most laptops will use lithium ion cells similar to the 18650 type in the battery pack. The pack should be labelled or documented with its nominal DC output and/or charging voltage, nominal current ratings for discharge and/or charge, and similar usage information such as temperature limits et. al.
Typically you'd charge such a lithium ion cell to a maximum of 4.20VDC with a more conservative end of charge voltage being in the ballpark of 3.75V DC.
The pack will contain some number of series connected cell groups and each of those cell groups will have one or more cells in parallel at each stage. So a 4S1P pack will have 4 series connected elements with each element having 1P or 1 cells in parallel. A 5S1P or 4S2P or 3S1P pack configuration isn't impossible.
Generally if you take the nominal listed battery voltage (e.g. 15V) and divide by 3, or 4, or 5 and you get a voltage that's close to 3.75V or 4.20V after the division, that'll tell you the number of series cells in the pack due to each series cell being listed with that nominal voltage value and the pack voltage being the multiple of so many series connected cells.
You'll have a pack positive power connection, a pack negative power connection, and usually one or two connections for a NTC thermistor which is mounted adjacent to the cells for the purpose of monitoring the pack core temperature. Charging or discharging should not be done outside of the listed operating range, e.g. -10C to +45C or whatever, and the powered circuit should use that thermistor sense connection to verify that the cells aren't outside of those temperature ranges at all times when the pack is to be used.
There may also be a "smart battery" set of connections following the SMBUS smart battery specification protocol -- DATA, CLOCK, GROUND. These connect to a gas gauge / protection IC in the pack and that protection circuit provides two or more levels of protection for over temperature charge/discharge, under temperature charge/discharge, over current charge / discharge, over voltage charge, under voltage discharge, and related functions.
If you operate the discharge and charge circuits within the limits set by the pack integrated protection IC you may be able to use the battery with a "dumb" load and charger so long as no protection limit is violated. If you violate some protection or safety limits the protection circuit may temporarily or permanently suspend or lock out either or both charging or discharging. For host/operator soluble conditions like an empty battery that is not unsafely undervoltage it'll usually just lock out discharge until charging is performed beyond some recovery threshold. To prevent overcharge it'll cut off charging current until the pack is discharged below a threshold etc. There are charge/discharge control FETS and fuses and a PTC protector and a current measurement sense resistor in series with the pack cells and your external pack power connection.
To maintain ideal safety and longevity you'll have to follow the pack's recommended and/or integrated protection / smart battery circuit's charge and discharge profiles as relate to temperature and charge / discharge current limits and state of charge. Look at the JEITA standard as well as the data sheets for common 18650 LiIon cells to get an idea about cases like high / low temperature charge / discharge, precharging, C/nnn rate charge and discharge recommendations, extended storage recommendations etc.
You may be able to access some of the details of the pack's information if you look up the safety certification test results for that pack model if those happen to be accessible.
Typically around 1A discharge currents and C/5hour charge currents (C = the mAh capacity of the pack) are reasonable. You'll generally charge at a constant current limit of say C/5 but also with a voltage limit of say N*3.75V where N is the series cell count in the pack. You can generally charge to 4.20V/series cell but that costs cell longevity and worsens storage life and recharge cycle life and makes it more likely you'll accidentally overcharge the pack if your constant charge voltage isn't precisely at or under 4.20V/cell.
See TI's web site for some gas gauge / protector product ICs like the bq20z75 et. al. to get an idea of what they do. If the pack supports it and your host can do so, using the SMBUS smart charging protocol will help you use the pack properly, though you may want to override its charging current and charging voltage limits with more conservative (smaller) values of your own.
More information --
Oh yes I'd forgot to mention that some packs have a system present line you'll need to ground to enable the pack to close its FETs. Some other packs go to sleep and perhaps open the charge / discharge FETs if the SMBUS data is inactive for too long and/or have no pull-up resistors.
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