I have a Rigid brand trim router on my machine and I need to use 1/16 inch bits for some engraving detail work. Is there any tool holder I can buy to chuck in my 1/4" router collet? I'd like to use some very small dremel type bits.

You may try to use something like this:

http://www.mlcswoodworking.com/shopsite_sc/store/html/smarthtml/pages/adapbush.html