Hi i love toilets!
I don't think there's an option to download only skins from the beatmap. But you can move the skin elements into a folder.
Here are some steps:
1.) Go to settings and search Open current skin folder. Once it's opened, make sure your filepath is set to ...\Local\osu!\Skins - you can check it by looking at the above tab where it shows Local > osu! > Skins >.
2.) Once you're in the correct filepath, create a new folder and name whatever name you like. Once it is done, go back into osu! and go through the beatmap's folder. (To open the beatmap folder: Go to Edit -> Go to your beatmap -> Click File -> Click Open Song Folder)
3.) You should see some images on the beatmap. To make it easier, copy all of the images except the background beatmap - any files that is a .png file or .jpg file - and paste them into the new folder you created.
4.) Once everything is done. Go back to your osu! and press the following keys altogether: Ctrl + Shift + Alt + S