Have done one - but it did involve cutting it.
Assuming you have already fitted the plastic 'bezel' from the old gaiter - if not, rip off the old one and swap it over. Then cut the stitching of the new one on the 'unseen' side of the gaiter. Obviously only cut the bare minimum you need so it just fits over. Invert it/turn inside-out and then make your choice of fastenings. I used (unbelievably) gaffa tape. Press/squeeze firmly for good adhesion. Bear in mind it won't take any serious forces, as there's the cable tie at the top. (presuming you have one in the kit, if not, trip to the Poundshop it is) But you may wish to get the needle and thread out, if you really want. Again, only rough tack stitches would be necessary. Cable tie the top, invert it back to the right way round, make it nice and neat, so the leather 'falls' into a nice shape, Clip the gaiter back and you're done.
Did it this way, on the old man's (now my) CDX TD 6-7 years ago, been in daily use ever since, without a problem.