Can I replace a microwave with a range hood exhaust vent without doing carpentry?
Having recently done the exact same thing you are mentioning, here are my tips and observations. For reference, this was the range hood I bought.

Make sure to buy a range hood that is the same width as your
microwave. This wasn't an issue for me since the microwave was a
standard size for most range hoods.
The only &quot;carpentry&quot; work I had to do was creating/adjusting the vent
hole in the bottom of the cabinet. The new range hood should come
with a nice template to show you were the vent cutout needs to be.
You may get lucky with being able to use the existing hole but I was
not this lucky. This was the ONLY cutting that I had to do.
The new range hood was super easy to install under the cabinet (4
screws!) with the included brackets. The exception to this is that
you may need to buy the cable that plugs into the outlet and directly
wire it to the hood.
You may have an unsightly backsplash area from where the microwave
was previously installed. I didn't have any paint behind the
microwave so there was a bare patch that I had to repaint. I also had
to fill a couple holes in the wall that were used to secure the
microwave.
You may need to get different ducting if the new range hood doesn't
include the appropriate adapter/connection for your existing duct.

Hope that helps!