Sounds like they are printing a paper check here in the states and putting it on a boat instead of a plane. Your vendor will not ship until they are paid so choose a different method, such as bank to bank wire transfer. Ask the vendor for their bank's wire numbers to his/her account (different than just a routing and account number) and initiate the payment at your local bank branch.
Other methods such as square, Paypal, venmo may offer international funds transfer but I am not familiar enough with any of them. Certainly, if the vendor accepts VISA/MC you could go that route and they would have instant confirmation and funds in their account normally within 3 days
