Welcome to the forum Kevin. According to the description you gave I think we are all assuming that your router has a trigger type switch so you'll have to strap it or tape it like Bob suggests. Once you do that you'll have to insure that you can not accidentally turn the switch on by bumping into it or any other means. To do so while changing bits would involve a loss of some finger mass. So use a switch that eliminates any possibility of that.
I've used a foot switch with mine at times, it's much more convenient that trying to fish where you can't see for the routers own switch but I've found that I have to place it where I have to reach for it so I don't step on it accidentally. When changing bits in that instance you should unplug the router. I also find the foot switch even more handy on my drill press where it's located at the moment.
Someone I consider a master woodworker once told me that a master woodworker is not someone who never makes mistakes. He is someone who is able to cover them up so that no one can tell.