I was able to get a cash advance on a visa-branded credit card in the main bank in Ashgabat, so I would imagine that any bank in the country could do the same for you. Just keep your receipt from the bank. I used a teller/live person and not an ATM. It was all very professional.
FWIW when I exited Turkmenistan, the customs people didn't ask/frisk me about money.
It's a tiny country. I'd recommend going through Ashgabat if only to see the spectacle of the "new city" (assuming you haven't already been...and it's on your established route that is declared when you enter the country.)