The problem that I see with a 'Sawsall' is getting the cut aligned properly for the replacement to be installed.
I just looked up "Sawzall" - it's a recipro saw - a DEMOLITION SAW! It's the sort of tool I'd use for roughing out a window opening in a wall or demolishing a stud wall. As you can tell, I think that it would be all but impossible to choose a less
capable tool. Unless you have absolutely massive sinks in the USA I fail to see how you will even get one into a sink to make the cut (I've used Hilti, Makita and Bosch recipros which is why I'm saying this - my experience of USA-style sinks, which are
larger than ours in Europe is, however, limited to a few installs). If you could get the saw in to make the cut how are you going to ensure that the saw blade doesn't damage the cabinets either side of the sink unit, and for that matter the water pipes embedded in the wall (or even clipped to the wall) at the back of the sink. I'd also be very concerned anout the amount of vibration a recipro saw is going to introduce into the countertop. With a recipro saw there is, I feel, the real risk of cracking/breaking the countertop to upstand joints.
I've got to say, equally that I'm not convinced that a Multisaw, such as the Fein is up to the job (and I own one of those for trim work). The 12mm (1/2in) Corian used to mould sinks is very tough material to cut and takes a lot
of power - hence my comments and those of others about needing a powerful router - and the little Fein just doesn't have that much power. They actually get pretty hot cutting timber so 30 to 40 minutes cutting out a Corian sink might well see one off (burn it out). I'll make a test cut in some 12mm Corian sheet offcuts this morning to see how quickly my FMM250Q will actually cut the stuff and report back
Using an unguided saw to make a cut like this will inevitably result in a really rough cut which will be all but impossible to disguise and which will make for real problems getting a good, leak-proof seal between the underside of the worktop/countertop and the new sink bowl. That's why the trade boys have developed the specialised tools to do this job