Wise is generally considered the cheapest option to transfer currencies. There are other methods, they are simply generally more expensive. For example, you can wire transfer the money, but this is quite expensive.

The supplier could also ACH your account using a payment processor that supports international cross-currency transfers... although this really isn't avoiding Wise. Most payment processors use Wise to actually perform the currency conversion, you'd simply be having the supplier use another middle-man and end up using Wise in the end anyways.