Is wiping with RNAse Zap enough to destroy RNAse activity?
It's hard to know what RNaseZap does since the ingredients list is a trade secret.  However, I expect it is a lot more than just detergent.  RNaseA is extremely hard to destroy; moreover it can easily renature once the denaturant is removed. Therefore, very minute quantities are sufficient to annihilate RNA experiments.  The historical method of purification was to boil solutions of it until all other proteins denatured and could be easily separated. I can personally attest that you can precipitate it in pure alcohols and it will spontaneously refold as soon as it is rehydrated.

I would not trust a simple detergent to get rid of it; you'll need something more volatile to be reliable.  A lot of "home made RNaseZap" recipes on the internet include hydrogen peroxide, which causes a variety of covalent modifications to the protein.  It also has the advantage of cleaning itself up (eventually turning into H2O).  The detergent is useful because you typically don't want any protein residue floating around your experiments, denatured or not.  If you have some dried RNaseA aggregates, it will also help break those up.  

I work with RNaseA itself, so I can't personally vouch for the recipe below (since I'm not interested in destroying my sample), but it seems sound.  But if you have the cash to blow, just get the RNaseZap.  It's very widely used by RNA labs and you really don't want to chance a potentially expensive experiment on it.  Especially since you're constantly shedding tons of RNaseA from your skin, being sloppy will probably bite you eventually.


Mechanism of action for H2O2
plausible recipe