Although adjusting your method of transferring stitches is probably the best solution, in the meantime you might try "liquid bandage" or "liquid band-aid". You just paint it on the affected part and let it dry and it forms a coating.
I used this years ago when I was doing a lot of quilting on a frame. Boy, did my fingertips get sore from the needle. The calluses that formed eventually helped, but meanwhile I used the liquid bandaid.