I've made some custom plugs before, but usually larger ones. If I decided I really, really had to do this, I would first get on the phone with the people at digikey.com to confirm it is custom plug and nothing like it is available. Then I would decide if I want to purchase a used Ryobi adapter off ebay or something and cut the plug off there to use. If that wasn't an option, then guessing it is too difficult to measure your pins diameters down inside the receptacle, I would order about three sizes or so of female pin terminals in the 2mm range.
https://www.digikey.com/en/products/filter/terminals-wire-pin-connectors/3972mm based on your penny in the picture with the N of "CENT" being in the neighborhood of your hole diameter. Once I have the right size female for snug fit and proper volt or amp ratings, I would solder my two wire lengths onto these female pins. Then I would slide the pins onto the male pins inside the receptacle, put masking tape or stretch wrap, or a combination of both over the receptacle area and right up to the pins. This is to protect it from the epoxy putty. I then would use a putty epoxy, one of my favorites is PCFix as in this link,
https://www.pcepoxy.com/products/emergency-repair/pc-fahrenheit/and make a plug shaped to be slightly larger than you want, around the receptacle area, around the female pins, and onto the wire a bit. When the putty is cured in 24-48 hours you can gently unplug it, sand and file it. Once you have the plug removed, you would probably want to add more putty around the female pins to keep them spaced and aligned and protected deeper into the receptacle. If it were me I would leave room for heat shrink tubing around the female pin depth that inserts into the receptacle, and a larger heat shrink tubing that fits around the plug and wire where your hand grips it. A couple months ago I did a video of the heat shrink tubing thing for an AC plug on a vacuum repair. I've been meaning to upload to wigglemylegs.com so maybe I'll do that today.
Then if this were to be an adapter, you would repeat a similar procedure for the other end that connects to your alternate power supply. Or splice this piece on there. Oh yeah, if you want to have a stress relief on the cable as it approaches your new plug, don't forget to slide the right size heat shrink tubing onto the cable prior to this whole procedure.
The other heat shrink tubes should fit over the completed work from the plug end of things.