Hi Again
Changing Scenarios and quite apart from getting from aircraft A to B depending on time & urgency I suppose it could be done. Although I note the Capt has only 737-200 experience & the FO -300. The -800 is a NG(New Generation) and as such quite a bit different to the 300 avionics wise but at the end of the day if it was life & death as long as you could get it fired up it would fly just the same as a normal aircraft & if - 300 speeds were used it would be on the safe side.(NG have different and more efficient wings)
Good Luck
GG