I have been on several dismasted sailboats over the years. The most graphic memory was when my folkboat lost its rig. We could not get around even crawling on the deck. I ultimately had to lie on my belly and move about holding on to stay aboard. A fully rigged folkboat has about as sweet a motion as any 25 footer that I have ever encountered.
I have also heard of bigger boats converted to trawler yachts but again the owners have done pretty extensive mods (bilge keels) to make the manageable. Properly closing up the cut offs or bolt holes, fabricating a shortened rudder etc will involve quite a bit of epoxy and buying a used powerboat has to be extremely less work than making the mod's even if you had to depend of family volunteers to scout out a worthwhile candidate.
I realize that an older boat with blown out sails have very little value, but the same boat modified as you suggest has negative value since someone will need to chainsaw it and take it to the dump when you are done with her. I don't know British tax laws but in the States you can also donate a boat for tax credits and that may permit you to buy a small power boat.
If you absolutely have your heart set on doing this. I would suggest that you have one of your volunteer family helpers launch the boat without the rig and see how bad that is.
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Curmudgeon at Large- and rhinestone in the rough, sailing my Farr 11.6 on the Chesapeake Bay and part-time purveyor of marine supplies