The transmitter doesn't "pair" with the ESC. It pairs with the reciever. As long as you don't need to change that, you should be fine. You will need to do a throttle calibration after the swap. The instructions will include everything you need to do that, which is a very simple process.
If you buy the 3700kv combo you will need to buy a pinion with a 5mm ID. This will limit you to running 32P pinions since its really difficult to find 48p pinions with a 5mm ID. So you would need not just a new pinion, but also a new spur. I reccomend buying a 50T 32P Spur (TRA6842) The spur is used on the 4x4, but will fit on the 2WD as well. As for pinion teeth, I reccomend starting with a 12T. Check your motor temps (finger test will suffice) and if it's cool after a hard session, go up to a 14T. Then just repeat until you're happy with the speed/acceleration/temps.
The 4000kv uses the same 3.175mm shaft like the brushed setup, so you can reuse your stock pinion.
I would reccomend going with the 4000kv just for overall ease. The swap is literally two screws, and the pinion is just one grub. It's much simpler to stick with the 3.175mm shaft.
I forgot to clarify your question regarding the motors. The numbers before the kv are just the dimensions of the motor. The 3700kv is 3660, it has a 36mm diameter with a 60mm length. The 4000kv is 3652, it has a 36mm diameter with a 52mm length.