Invite his mother, grandmothers, and sisters no matter what (unless you end up also having a local shower to which they will be invited). After all, including those who are going to send a present no matter what isn't gift-grabby - it's not like his mother wasn't going to get you a baby gift, right?
The aunts, cousins, etc, could get tricky, but if possible I'd leave that up to MIL or a similar matriarch. I'd just explain that I don't want to look gift-grabby nor do I want anyone to feel excluded, and is there anyone she thinks would be hurt by not getting an invitation? Then I'd send invitations to those people. (If I didn't trust her judgement, I'd skip asking her and leave it at MIL, all SILs, and his grandmothers.)