I cannot answer your question, but, in general, most smaller shops tend to be rep-friendly. Your best bet is to google watchmakers in your area & phone them to find out.
Love this pic. It caught my eye during the wristies.
I know how much goes into these '42s & this perfectly typifies what is possible if you have the testicular fortitude (& cash) to stick with it.
Good, clear macros pics of the date wheel & related components &/or the movement model be very helpful, but also check to be sure you have the correct date wheel & calendar ring for your specific caliber & that the ring is fully seated onto the pillar.
36mm, for a Rolex, unless you're a trend-conscious fashionista (as opposed to a gentleman with classic style), is not petite.
While I prefer more vintage models, there is nothing wrong with that Explorer. I say sate your desires.
When dealing with non-gens, I would not assume anything. The only way to know what fits your particular case is to try it. Sometimes a gen or aftermarket tube will fit perfectly, more often you may need to re-tap threads to make them fit (the crown must fit the tube, not the case).
Depending on age, the 6263 was fitted with either Twinlock (early) or Triplock crowns (later). Golds will be pricey, so be prepared.
Tube should match whichever crown you use (the part of the tubes that screw into the case are the same). Typically, the crown seller will have tubes, or you can get them from most of the watch parts houses.