Myles, The only Healey I have done was my own, but they are probable all pretty much the same. The outer sill or rocker has an extension at the rear that goes behind the rear fender ( it is about 4 or 5 inches long and can be seen when looking on the inside of the lower rear fender from the wheel openning) and the front has a small extension that just gets behind the front fender. So at the least it seems to me that you would have to unbolt the lower edges of the fenders and on the rear fender you would have to unfasten the leading edge of the fender where it is fastened to the door shut pillar. This seems to me to be the hard way to do it and I suspect that even if your car shows no sign of rust, there will be rust when you open it up. If the lower edge is rusted bad enough you won't have any solid metal to tack or spot weld the new sill along the lower edge. But the rear fender does come off easily, just reachable bolts along the perimeter. And the front fender can be loosened and pulled out quite abit by just unfastening the lower edge.
Having said all this, a production body shop would do the job in the fastest way possible. If the lower edge was rotted they would weld a strip of metal there. They would pull the fenders out just far enough to force the new sill in place and tack weld it anyway they could to make it stay. That doesn't do anything for badly rusted surfaces that are just passable. If you just have dents and don't want to go through all the reconstruction, I would fill the dents with body putty. There are a variety of excellent fillers that are "Extremely" durable and will last as long as you own the car. Well, that's my two cents. Good Luck, Dave.