@Mark_S I expect the security relating to the desktop is an impediment to paste from clipboard but I would just share with you a substantial if only partial solution.
I have designed a range of copy to clipboard buttons I can install in my TiddlyWiki’s, but in doing so I also copy to “clipboard tiddlers” so I can paste from a built in tiddlywiki clipboard. With a little extra effort I could drag a clipboard with content across wikis as well.
Also another avenue is automated construction of bookmarklets as a clipboard with content. Just drag to bookmarks and Jump to the target wiki and click to paste. Then have a paste from tiddlywiki clipboard where every you want.
Also using a save as json and easy workflows to import is also a good alternative in many cases. Ask if you want to explore how I could possibly suggest this, my expertise in Window’s only.
Finally, a related tip on windows rather than ctrl-v to paste using windows-v allows you to see the clipboard history. So although we can’t control the paste (ie pull from clipboard) it has additional features.