I've used a combo of shoe goo and zip ties to securely hold together cycling shoes for a while, but wouldn't really recommend it. Shoes are a safety critical device . . . you don't want to be 100 miles from home and not able to pedal properly, or to have your shoe tear off when you stand up and hammer the pedals, or to have your shoe not release properly when you come to a stop light.
So unless you're really attached to these shoes for some reason, I think you might be better off to just get a new pair of shoes. Good cycling shoes can be had for 60-70$ and will last you quite a while.