KrungSri has Western Union ability to receive money from WU sender into Thai bank account, or send money from Thai bank account to WU receiver. You might have to set it up at the branch once (or within online banking).
Krung Thai also has this ability. When I looked at it [2-3 years ago], it was fully integrated into their online banking platform.
Technically, it seems that you could sign up directly via Western Union's Thai website.
But I would advise to go through the motions of your Thai bank's online service or via the mobile app first. They already have all of the verification integrated to where you just accept a few disclaimers and then you should be ready.
You may need to confirm transactions with OTP via SMS to Thai cell number associated with your bank account. So make sure you retain your Thai sim card with sufficient validity to receive these SMSs (which are free even when roaming overseas).
Also might be a good idea to do a test spend with someone in Vietnam (while you are in thailand, before you go). If you could sent it successfully, it should work for yourself also.
And before you balk about WU's fees, there are special pricing for the APAC regional transfers from Thailand. 300 baht to send up to 30k baht, 600 baht to send up to 100k is pretty reasonable (considering most alternatives).

I sent money to Ukraine and it was 1500 baht fee. So take advantage of the cheaper regional rates.
I don't think transferwise or [cant remember the name] would work in your case, since you need a bank account to send funds to. I don't think you can send baht out of thailand into TW's borderless account. And of course with SWIFT transfer, you need recipient to have a bank account also.
Getting your money back from Vietnam to Thailand is a separate issue.
Generally speaking, the lesser developed country/economy wants to hold on to money and prevent too much of it from being transferred out without a reason. Maybe someone else can better answer this one as I have very little experience for outbound Vietnam transfers. Especially without a local bank account.
Re: Bounty question:
Hello again dear Jon. I now offer 100 rep bounty for another two issues very associated with this: I think to close my Kasikorn account because the Krungsri account is my main one I use and I really like Krungsri's application security model (and design) and from my minimalist ideology; also, knowing that Krungsri have Western Union partnership and Kasikorn doesn't (for a few years now isn't it?) is even more pushing me to stay only with Krungsri
But, as we both know, Kasikorn might start to have it as well "tomorrow" and re-opening a Kasikorn account would probably not be very easy with certain visas. I plan to change my family name while in Thailand and therefore, if I go to the bank after that, I would have to bring new passport (containing previous family name and old passport number), and maybe also a notary letter approving the change) for both banks to change the family name in their systems; but I'd prefer to first closing one of the account and only then changing the name so system change would become only in one bank
Given all these data, do you think I should close my Kasikorn bank account or just leave it empty with no money in the background and don't hasten to change the name in Kasikorn's system?
IMHO it's always a good idea to have more than one bank account available, across at least one other bank.
It's better to have the account and not need it, then to not have the account and wish you had it after the fact. Consider:
You have assets spread out in Home Country + Thailand + Vietnam + other countries. Or you need someone to pay you. For whatever reason, you may need to be paid under the old name.
2) Even if you eventually must update your name everywhere, you have the option of having a separate account should there be an issue with the other account. (anything from a network issue to a feature suddenly being unavailable).
3) Better exchange rates at one bank vs another for receiving int'l SWIFT transfers (hint: TransferWise is your friend)
It doesn't necessarily have to be Kasikorn, but since you have Kasikorn, I will admit that their topup and transfer integrations into payment systems like Lazada wallet or even PEA electric bill payment are very simple compared to other banks. Even topping up a phone or transferring to another person there is less clutter. The cardless withdraw is nice also (within Thailand). It's one of those things where one bank might have a slightly different implementation of a feature that you either like or hate. But having options are useful but not 100% desirable are much more preferred to not having the option at all and needing it.
The only disadvantage to keeping an account open is having to pay annual fee for debit card. And possibly fees for other services, such as alerts.
- You can cancel the debit card (just use cardless ATM) or do online
transfers.
- keep the debit card and set purchase limit to 0 (until you
need to use it).