If I was in that position, I'd either use regular shoes and pedals (maybe with Power Grips straps). OR, I'd simply use walkable MTB shoes with SPD-type pedals. Buy whatever shoes seem to fit your needs. A couple of friends have SPD shoes they use for general cycling that look more like heavy sneakers/ light hikers than bike shoes.

I personally would never bother carrying shoes - Id pedal in shoes I could walk in.

(PS: if you carry all that stuff around every ride in a backpack, you really should get a rack and a little removable bag to put on it. Much better than a backpack).