A dremel tool works great using a cutting bit. But the problem is going to be aligning the chain plates properly unless you made a template before hand. If a template was not made before hand you can use duck tape on the underside and fill from the top with a silica compound where you over cut.
When I re-bedded the chain plates on my islander I left them attached and poured around them. As the process begins to harden they can be tapped out if desired. Made for a solid bedding and sealed fit.
Both a dremel or a router would work depending on how much room you have to work with. The problem is going to be proper location of the hole. I would mark the location inside the boat using the chainplate as a guide. Then use an extra long 1/8 inch drill bit to drill holes at each end of the mark. Put a little grease at the midpoint of your index finger and thumb, and bend the bit to guide it alongside the bulkhead. This way you can ensure that the hole you cut is directly above the bulkhead and the correct angle through the deck.
Edit: Make sure you bed the chainplates properly with butyl tape.
To make the hole, I am going to use my drill for the ends and my Fein multimaster for the plunge cut on the straight parts. I am going to use my dremel with a 1/4 inch sanding barrel if and as necessary to clean up anything that needs it.
I am then going to use the sanding barrel on the dremel to chamfer the top of the hole and use butyl tape to seal.
Good Old Boat had an article from Don Casey about 2 months ago where he raised the chainplate hole off the deck by building a mold out of clay and filling with glass and epoxy. He basically built a small 4x4 inch platform around the chainplate about 1/2 -3/4 inch high. This way any rain water running down the deck will go around the whole thing and not even test how well the sealant is working. I may try this. Stay tuned.