I think cod is right 2.2 HP may struggle a bit with a boat that size if the chop is bad enough to genuinely justify a cat c boat (oh oh - thats probably just started a third thread debating the value of the RCD
I don't think you will need to go as big a 7.5 HP though. Whilst it would be nice to think you could get the rib on the plane if you wished to do so lightly loaded - what you are interested in is getting from your mooring/anchorage to shore and back. Essentially in rib terms (or at least in terms of most ribnetters) this is just an auxilliary engine. The generally ribnet rule of thumb is 1HP per m of hull length for an aux. So a 3.3 should be OK. A bit bigger would be slightly better - but bear in mind that bigger will be more expensive and probably heavier.
In terms of hull - i think you have 3 options: (1) a totally soft bottomed boat (known as SIBs here). (2) a soft bottomed boat with floorboards (also known as a SIB) (3) a fibreglass hulled boat with inflatable tubes (what is generally considered a RIB here).
Depending how big your yacht is will influence which of these is sensible. But my experience of yacht tenders in category 1 above is that they are much less "secure feeling" than the sort of thing I think you have right now - but as cod says much easier to collapse and take with you.
Not sure if there is anyway you can try these afloat before you buy. Stepping down off a yacht can feel quite tippy in a lot of boats.