The Mugen cap winds up recessed below the red beauty cover and you may need more room for fingers than is available.
I have an Mugen cap eBay replica on another Honda and checked the fit a while back. BTW, the eBay replica cap/gasket was cheaper than a new OEM cap gasket alone.
I've been running a Mugen oil cap since I got my car, although I haven't run the engine cover since day 2 and can't tell you about any issues with interfacing with the OE engine cover. Everything works and fits fine.