Step 1.) Unmerge Calyrex and the Horse.
Step 2.) Clone them.
Step 3.) Trade the clones to your OFW Switch.
You don't need to break the game to do that... nonetheless you can never have properly multiple forms on the same save because of...
As you stated prior, the 3 Fusions in the Pokémon series are all the result 3 Pokémon each having forms requiring Fusion to transform into. The 3 Pokémon are all available in Sword & Shield and are: Kyurem, Necrozma, & a Calyrex.
What you are missing from this equation is how the Fused Pokémon unfuse:
The Fusion mechanic for all 3 of the Pokémon is the same. The game has 3 invisible PC storage slots; one for each of those 3 mons. When the Fusion occurs, the "other" Pokémon is deposited into said respective indivisible PC box. The trade restrictions on those 3 Pokémon's fused forms from being traded because a player would loose the ability to ever withdraw the "other" Pokémon.
While the Encounter Mod, allows CFW users to encounter illegal forms (including all of the forms of the 3 fusion-capable monds)... the game is not programmed to assume you cheated. So, you were able to obtain this illegal form without depositing the "other" Pokémon into its invisible PC box... but once again... the game has no idea you cheated that result.
The trade is where you should be able to figure out this would require and ONLY work between two modded games on emulation or CFW devices. You will never be able to use a CFW game to "hack into" a legal game. If the games are not both talking the same "language" (it's metaphor here) then they will just produce an error in the communication process and disconnect. You will need to find a modder and convince them it is worth the effort.