Yes, you could upgrade engines. The initial four Britannia 737-200s were delivered with -9 engines and G-AVRN - the one which served for the longest with Britannia - was upgraded to -9A through time. If I remember rightly, one Dan-Air 737-200 flew for several years with a -15 engine on one side and a -17 on the other, although I'd imagine they would have had to treat that as a -15 aircraft for performance calculations.
For the range and capability, bear in mind that there have been many changes over years to standard passenger weights, the level of reserve fuel required to be carried and airfield performance safety margins. The regs still permit IT charter standard passenger weights to be differentiated from scheduled ones, but both sets of figures have gone up quite substantially in the last two decades. If you took yesterday's aircraft and applied today's performance rules to them, a lot of things that used to take place would either be impractical with a viable payload today or just wouldn't happen at all.