We use a skip hop bag for DS at daycare and recently bought another to replace the nappy bag.
They aren't a huge bag so it would depend on how much you would need to fit in.
For daycare (the bee bag) we can easily fit a change of clothes, hat, sunnies, suncream, aeroguard, ventolin +spacer
For going out bag (giraffe) I can JUST fit a cooler bag, nappies, wipes (in the front pocket), nappy bags, hat and sunscreen
Is there any way you can get to a shop that sells them and have a look? (I bought mine online interstate).