If you have the player use a Sharpie and sign it on the numbers, you should not run into that problem. I have a game worn jersey signed with a grey Sharpie and two authentic jersey's signed with black Sharpie makers and none have that issue. Make sure to never use paint based makers, those tend to bleed over time.
I normally will not wash the jersey once it is signed, but one time I did and as the previous poster said, it did not smear the ink at all (black sharpie on white #) .. Other than that I'm not sure how else you would preserve it. If you hang it up or get it framed, it will stay the same forever.