I would test the water (or take it to the LFS
and see if they will test it). Depending on what the results are, make a decision on the water change. I would not do more than 20 percent at a time. You would be better off doing a small percentage each day, if you need to, to get the water parameters in check. That will keep your fish from stressing from a sudden, noticeable water quality change.
For the move, keep as much water as you can. Put it in buckets, rubbermaid tubs, etc. Put the fish in a bucket or tub and try to get an air bubbler for it. Same thing for any rock you have. Hopefully it is a short move.