You might not believe this, but I pushed my folder from Cairo to Cape Town on a pair of flip-flops. Nothing more. I had a pair of shoes with me, but mailed them back home in Nairobi as I hadn't used them once (pushing weight is always an issue of course). I can probably count the times I wear shoes in a year on my 2 hands. Flip-flops are basically the only mode of shoes I ever wear.
So the only shoes you need to pedal your folding bike, you can find on www.footbrake.net. Yes they might be the right shoes when you need a 'brake' from cycling, but I suggest you wear them all the time!