I need to replace a single bowl sink with no drainer for one with a drainer on each side (because the wood has been water damaged beyond repair). I don't have much worktop so if I do a full cutout, there won't be much left to support the sink. My possibly daft idea is to cut a channel in the worktop around the drainers so that the sticky-up mounting bit (see pic) can drop into it, leaving the drainers supported by the worktop. I might need to cut small holes all the way through for fixings, and I'll need to seal it, but it's fine for it to be a bit of a bodge, it's a temporary measure while deciding on proper renovations.
Would this work?
Would this work?

