The control rout on my son's '04 Affinity Special was deep enough for the better switch I installed. It was a CRL or similar, it reached deeper than the stock rectangular switch.
The stock pots were 500k, I replaced them with CTS 250k pots and had to enlarge the control plate holes slightly to get those to fit.
I didn't measure the knobs, but didn't get the impression they were smaller outside diameter than others. They have a somewhat smooth grip, I prefer the more coarse grip of the knobs Fender puts on MIA/MIM Teles. So I chose solid shaft pots and bought the more coarse feeling Fender knobs, and installed them together.