Making OGC WMS/WFS look like ArcGIS Server layer, including functionality?

Since you have put a bounty, let me try to explain why you are not likely to get a favourable Answer.

For your WMS/WFS services to appear as an ArcGIS Server Services, the Intermediary wrapper must implement, what ESRI Calls the GeoServices REST Specification

If you take a look at just the specification, it is vague in many respects. There are many other criticisms of the Specification, most of which are covered in this document Geoservices REST API critique.

Hence For your Wrapper to appear exactly like ArcGIS Server, you'll have to reverse engineer the REST API of an existing deployed server. That is easy enough. you just need a running ArcGIS Server, a browser, and firebug/Wireshark. Whether it is Legal, is a different question, one I am not qualified to answer.

If you ask if there is any current open Source software that implements the GeoServices REST Specification, the list is very short. The people at OSGeo, could only find one software: Traveler-Info-GeoServices-REST

Given your need for a Wrapper, your best option would be to write one/ get one developed. You should also look at this question: How can I implement ESRI REST API?