@Bonnie ******
Sending the money to your Krungsri Bank account via SWIFT wire from your US Bank should work just fine. It will be labeled correctly as an international transfer originating outside Thailand. It's only a problem using Wise with Krungsri Bank.
By the way, Krungsri is an easy bank at which to open an account (maybe the easiest) and they have a really nice savings account Mee Tae Dai paying 1.00% APR interest. Money transfers visa Wise are just not reliably marked as being international. With Bangkok Bank they are (as long as "for purpose of long term stay in Thailand).
Wise does not use Krungsri as a Thai partner bank and therefore Wise transfers from overseas are more than likely going to show up in your Krungsri Bank account as domestic transfers from another Thai bank. This leaves you in a position of explaining to your immigration officer that while it's labeled domestic in your passbook/bank statement it's "really" an international transfer. I would not relish being in that position. With Bangkok Bank that is not a problem.
Please see the TransferWise Solutions Thailand group for the lengthy explanation and the gory details of why this is the case. The short synopsis is that Wise is able to do transfers economically because in many cases it is able to accomplish your "international transfer" by doing a domestic transfer between its Bangkok Bank Thai corporate account and your Thai bank account. When your Thai bank account happens to be Bangkok Bank this shows up as a FTT, an international transfer. When your bank is another Thai bank it often shows up as a domestic transfer. You then have to demonstrate that while it shows up as a domestic transfer it's really an international transfer.