You only need the PK of your receiving wallet. A wallet basically is just your PK (that’s why you should never share it). If you have the PK of the wallet on BSC (Binance Smart Chain - the blockchain not the CEX) then you can use the same PK on Harmony and access the funds.
If you sent it to “your” Binance wallet on the wrong chain. You don’t own those wallets, Binance does, so only Binance could potentially help, but normally they won’t (I assume also that they can’t as the CEX’s wallet PKs should be secretly stored somewhere)