Given your comment that it's that it's stranded then i'd suggest going with two plugs and a coupler. If you want to run high speeds then getting a coupler that is actually cat5e rated rather than a generic RJ45 coupler with no internal impedance control is probablly a good idea.
Punch down connections are only suitable for solid cable. Soldering and heatshrinking is possible but will create an impedance bump which may cause issues at higher speeds. The jelly connectors that telephone companies use will likely create an even bigger impedance bump than carefully applied solder/heatshrink and are also unisuitable for stranded cable.
When you use TIA/EIA-568B on both sides this is a straight through cable. The colors of the inner jackets don't really matter, much the same as it makes no difference to the operation of the network if you use a network cable with a black or yellow outer jacket.
However, the standard is in place for a real reason, and that is that the cabling system should be implemented in a standard way so that anyone who works on it will intuitively understand what they are working on.
For instance, imagine if someone used your reversed wiring in a real environment, left, and you were now troubleshooting a cabling issue at that site. On inspection, you determine the cable is damaged and it need to be re-terminated on one side and did so with the standard TIA/EIA-568B. After doing so, the cable still will not work.
It isn't because your termination is bad, but because the cable is now a rolled cable. You may waste additional time/resources on trying to re-terminate the cable additional times. Unless you use a cable tester, you may not easily figure out that the cable is now a rolled cabled.
Ultimately, this potentially causes more problems/downtime and isn't really justifiable by any possible reason the original person may have had to not follow the standard.
Old answer (thinking the OP was talking about using TIA/EIA-568B on one side and the reverse on the other):
What you are describing is what is often referred to as a "rolled" or "rollover" cable. Pin 1 connects to pin 8 on the other side, pin 2 to pin 7, etc.
This type of cable would not work for network communications, but is used by many vendors for serial communication, such as console port access.
Best Answer
Cat 7 is neither UTP or STP. It is typically either F/FTP or S/FTP.