iPhone 6s motherboard swap question

I have two iPhone 6s devices: one in physically great shape, but with the new iOS (which I hate). The other has the old iOS but a slightly warped case, which means the screen does not fit clean (happens with other screens too, so I assume it’s a case issue not a screen issue).

I would like to swap the motherboards so that I could use my preferred iOS in the nicer phone. This looks easy to do but I have read that fingerprint ID becomes unavailable. If I switch the motherboard AND the screen, will this solve my problem and allow me to use touch ID?