The TOS shuttles clearly had warp nacelles. I fail to see how people could ever pretend otherwise.
The Kelvin shuttles (which also had obvious nacelles) *had* to have warp drive, otherwise Nerada would have had plenty of time to recover from George's ramming and kill everyone.
Some of the nuEnterprise shuttles had warp nacelles but not all (also: watch as Kirk and McCoy board a shuttle of a different design to that they land in!).
I was mildly suprised to see a 2258 shuttle with a transporter - but those shuttles closer in size to a runabout and the NX01 transporter didn't take up more than a niche in a corridor. For all we know there was a transporter in that little room at the rear of the TOS shuttles.