Get yourself a vintage set of bicycle shoes, often times available on Ebay. Fit is a hit or miss thing, when buying this way, but you will, at least, have a proper hard sole and you do not have to use cleats, if you choose not too.

Just did a "shoes" search in vintage cycling, on Ebay. See if this creates any interest, for you.

Or, check out the Classic and Vintage forum, for sale section, and you just might get a set even cheaper and with less risk.