Firstly I'm almost certain that Galactus directly lifting or wielding Mjolnir hasn't yet been depicted. So we'll have to go back to how the hammer was made and how its magic works. The hammer was made from uru metal and enchanted by Odin whose enchantments would be backed by the Odin force which is one of the most powerful things in the marvel universe. Now in order to wield Mjolnir you must either be found worthy or have the strength to overpower Odin's enchantments which would be a impossible feat for most anyone.
Galactus himself like the OP mentioned isn't exactly evil well this is true but it goes further than that. Galactus as long as he isn't hungry is a rather peaceful entity, even more so he exists for the purpose of recreating the universe when its time comes, like he did the last time he does feel some remorse for the planets he eats in the same way people might about eating cattle. So it could be a toss up if Galactus is actually worthy or not everything he does is to keep the universe alive, and facilitate the creation of the next one. I got this Galactus info from the marvel wiki page
Now the worthiness may not actually matter if Galactus is strong enough to break Odin's enchantment which is another one that could go either way as there are times where Galactus and Odin have rather epic fights without a clear winner. Although I'd say that if Galactus' power cosmic would be able to overpower the Odin force's enchantments on Mjolnir he'd be able to wield it. This would be like the unstoppable force immoveable object debate.
I also want to add that this is Galactus' and he could easily move the hammer about in a number of ways, but to actually wield the hammer in the same way that thor does would take more effort from him and may not be possible. There are also other things Galactus could do instead such as just creating a copy of the hammer with his own power but lacking a worthiness requirement or a different one. So technically Galactus would likely be able to move the hammer but not actually wield it, not that he would ever want or need to.