I'm terrible with the chisel and wondering whether a router can be used
to make moretise cuts for hinges. I imagine that you would need to have
curved corners in the cuts. Is that so? In that case, do there exist 1
1/2" hinges with curved corners?

Many thanks in advance!

As others have said, you absolutely can to this. I use a slightly different
approach. You can buy or make a template, but I don't do it that way. I use
my "trim router" because freehanding with a router makes me nervous and
smaller is easier to control. The bite that you need to take for most
mortises is pretty small so even the smallest router is more than enough.

I mark out the mortise just like as if I we going to chisel it out by hand
(except no need to mark the depth) and the hog out most of the material
freehand. I then clean up with a chisel.

The base of your router should be twice as wide as your hinge so that it can
be well-supported. If you are routing the thin edge of a board, it held to
clamp a board along that edge for a little extra support.

Try one on scrap first to get the hang of it and you will fine it to be
pretty straightforward

-Steve