OMG, for safety reasons, do NOT hide an AC cord behind the baseboard! That is a gross safety violation!
AC "Extension cords" are meant to be temporary, visible, not hidden, not under a carpet, etc. certainly not inside your wall or behind a baseboard!
Yea, we've probably all wire-stapled some extension cord against some molding. (But hopefully not as an adult...)
Extend the DC cable from the adapter to the router, instead.
Get a small shrink-wrap tube assortment. cut the wire, splice-in an extension (you might want to use a heavier-guage wire depending on how long this has to be).
Make a proper wrapped splice (make an "x", wrap the ends along the wire in opposite directions - if you tug on it, it should tighten rather than come apart), and solder, making sure you heat the WIRE, not the solder. Heat the wire and feed solder into the junction. The junction must melt the solder, not the soldering iron.
Slip a piece of shrink-wrap tube over each wire, and a larger one over the whole thing. You should be able to make a splice with a minimum of bulge if you are careful. Slips the shrink-wrap over before soldering.
For a small job like this, you can use a match or lighter to shrink the tubing. A hair-dryer is not hot enough to do the job. There are special heat guns, which are overkill for making one extension. Don't kludge it with electrical tape.
