I used to live in Providence and Boston. I miss that area this time of year.
I'm not sure where the CC rail trail starts, but from Providence here's how I would go to the Cape:
Take the East Bay bike path from East Providence (not Eastside) down to Bristol
Keep heading south on 114
Bridge crossing on 138, but get off 138 as soon as you can after the bridge.
Head south, and get on 177 (American Legion Hwy)
By the Westport factory outlets, get on Hwy 6 (State Rd.)
Take 6 all the way to the Bourne Bridge and you're on the Cape.
Alternative routes would take you much further north through Taunton, or so, so my preference would definitely be taking the above-mentioned route. The two worst points will probably be the two main bridge crossings on 138 and the Bourne Bridge. Good luck and post a trip report when you get back.