The only answer is to simply use ofx.com (or a competitor such as transferwise.com)
Sending a "wire" is laughable in the US. Don't even bother.
(Don't even mention that the exchange rate you'll get is crap.)
It's a nuisance to set up an account at ofx or the others, but once it is in place, everything is dead easy, one click.
Source, we do this ...
Definitely not the only way.
Most banks will write you an international bank draft (like a cashier check but in in any currency), payable to anybody. They might mail it direct to the company, or mail it to you so you can mail it to them. This is usually the cheapest way to send large amounts.
If it's a large company they may have a US branch or a US dollar ...
Avoiding any financial reporting threshold is a crime, perhaps even imaginary ones via "conspiracy". Either way, according to the Treasury "The Internal Revenue Service Still Does Not Make Effective Use of Currency Transaction Reports"
And this was before the IRS got ...