You first want to pick the non-workshop ROM hack you want to use, for example I used Shadow in Sonic the Hedgehog[info.sonicretro.org]. Download the ROM and then download a mod off the workshop that's for the game that your non-workshop ROM is (I used Pantufa the Cat). Locate it in the workshop files folder for this game's appid, by default it's

C:\Program Files (x86)\Steam\SteamApps\workshop\content\34270

You want to look in these folders until you find the .bin file named after the workshop mod. Delete that file and replace it with the .bin file from the ROM you downloaded at the beginning. Now that you've done that, you should be able to load the mod in-game with the name of the original workshop mod. When it loads that mod up it should instead be the non-steam mod.

Congratulations, you have successfully installed a non-steam mod for SEGA Classics