I'd say this depends entirely on the DM's concept of undeath and how he will rule on the question. If he rules that undeath, because of the tie to negative energy, is inherently evil and corrupting, regardless of the intent and efforts of the character, then it could be a problem for the paladin. If he rules that the fact of the undeath doesn't matter, and alignment is based purely on intent and behavior, then it's not an issue at all. I agree with others who have said that a positive energy mummy would sidestep the "undeath" issue.
On the other hand, there are some cool role-playing opportunities with the "undeath is inherently evil" approach. You have a situation where the mummy wants to be good and tries to be good, but can never completely overcome his basic, corrupt nature (kind of like the massa damnata concept). Much would then depend on the players, the DM, and the fantasy theology regarding morality/sin/alignment. That could be really cool, or really, really frustrating. Everyone would have to be both on-board (i.e. willing to try it out) and also hopefully share an understanding of the "fantasy moral theory" for it to work well.