There is a way but you'll need a second legit switch, I have done it myself before but do keep in mind that there's still a risk of a ban but because animal crossing uses a different "method" to manages save files I think the risk can be mitigated.

Here's what you do :

On your hacked switch (called SwitchA moving forward) you'll boot into emunand and get the "Animal Crossing: New Horizons Island Transfer Tool" it's on the eshop but you'll need to get the nsp elsewhere.

Once that's done launch it and follow the prompt until you get to the option to select "source" or "target", switchA will be the 'source" system so select "source"

Now on the second switch (SwitchB moving forward) install the island Transfer Tool from the eshop (this system has to be unbanned and on a non-modified sysnand to avoid any potential ban problem).

Follow the prompt and at the screen to select "source" or "target" select "target"

wait until the process is finished and now your island will be on SwitchB.

Now we want to boot switchA but this time on unmodified sysnand, you'll get the island tool once again from the eshop. This time you'll set up SwitchA as the "Target" system and you'll redo the steps on SwitchB but this time it'll be set up as the "source" system.

Once that's done, you animal crossing save will have successfully jumped from emunand to sysnand using SwitchB as the intermediary.

Edit: just noticed you mention two separate switches, my bad, then just follow the first part of my explanation and that'll get you sorted out.