Electronic – Two way switch, original was 16 AMP, can I use a new 10 AMP

In your design, assuming you're using a common small signal NPN BJT (2n2222, BC547, 2n3904…), you're wasting about 20-30mA of current when the switch is closed. That is, about 10-15mA through the upper 220Ω resistor and 10-15 through the lower one. In addition, driving the base of the transistor with 10mA or more in this situation makes no sense: using a 10KΩ base resistor and thus reducing base current makes the circuit behave almost in the same way. That said, I would just avoid using the transistor, something like this should work:

^{simulate this circuit – Schematic created using CircuitLab}

I kept your values for R1 and C1, so the cutoff frequency of the circuit is similar to yours. I.e., the GPIO pin will not 'see' changes of the switch above about 5Hz (well, simplistic and not completely exact: see Wikipedia - Low Pass Filters for detailed info).

R2 is used as pull-down resistor: it is useful because it clearly pulls the pin to ground when the switch is open. Its value isn't critical, something between 10 and 150KΩ should be ok.

There are more things to consider.

First: Note that the vacuum taking only 1100W, i.e., 5A, could still draw a very short peak of much more current when the motor starts; it really depends on how exactly are these 1100W calculated.

Second thing: Is the 13A fuse in the cleaner accessible? Could you exchange it for a 10A fuse? The only thing that can happen then is that the fuse blows up unexpectedly.

Third thing: Is spending couple bucks for a 15A rated switch that much a problem?

While I don't think your house will catch fire because of this (since 1. mostly when something goes wrong, the current drawn is much higher than what it should be and should blow up your 13A fuse and/or your circuit breaker long time before the switch heats up to ignite and 2. the 10A rating of the switch means it should withstand much more in practice, there's a certain safety margin), I wouldn't recommend violating the rules of the game, since in this game, the game over could be quite serious.