It shouldn't be a problem. If the work piece in which you are cutting
the hole is small (providing little support for the router), you can
place some supporting stock around it. I usually use a piece of 3/4"
plywood as a base, then place the workpiece and some auxillary support
stock on tope of the plywood base. I'll use carpet tape and/or brads
to hold everything in place. I'll also use F-clamps to hold the base
on the bench. The base is sacrificial. I make sure that the center pin
goes through the workpiece and into the plywood base. This prevents
accidents when you cut through on the last pass with the router.

Your question is a good one, because the success of cutting clean
circles with a router is totally dependent on everything being locked
down tight. Don't depend on holding it with your hands.

Bob