I have experienced this kind of problem before and exactly the solution to this problem is as follows; some addresses use a different derivation path if you selected your deposit address from signable addresses, not to an address that Ledger automatically provides.
When using P2PKH with ledger live, you only get P2PKH addresses.
When using P2WPKH nested in P2SH, you only get those nested P2SH addresses.
There is no bug or similar where you get a legacy address in a nested segwit wallet in ledger live (or vice versa).
As stated in the OP:
(I've also doule checked twice the address the wallet gave me where to send the btc)
So your proposal is highly unlikely to work and shouldn't be tried by OP without confirming that he was using a different type of address than usual.