I have found that almost every business will require a reservation in advance if there is going to be a party. You cannot bring food or drinks into a business without their consent. So if you do decide to reschedule it you will not be able to do the cake and any other activities.
If you go bowling you will need to just take them and pay for the lanes and that's all. They wouldn't even let us do presents at my oldest grandson's birthday. We had reserved the area for parties and in a mix up they lost the reservation. We had a bunch of people show up and I had cake and drinks, they made us take them out of the building. I told them we had reservations but since they couldn't find it they said we didn't have one. So we just bowled and took the cake and stuff back home with us. It was still fun.
McDonald's, Burger King, any fast food place, they are going to charge you and they may already have a party going on where you can't even go on the playground.
So if it is raining I suggest the movies or some other activity but if you can't do it at the park you may not be able to do the cake, drinks, gifts, etc....