Are the shelters large? Typically in S. Cal, rain isn't very heavy, so if the shelters are large enough to keep your guests and gifts dry, and the grills are going to be going to keep people warm, I think it's fine. If not, I would plan something indoors to keep people comfortable. Do you have a community center you could use so that you can set up the party indoors but still be able to grill outdoors? That might be the best of both worlds...
If you haven't already booked the park, try looking around for ones with a rec/community center or an HOA community center/pool house. They're typically inexpensive to rent.
BTW, I think a baby-q is a super cute idea!