If you don't have checked baggage, you can try to get a boarding pass for your flight to Vietnam at Air Asia's airside international transfer desk at DMK. It might or might not be possible, having two separate tickets, but it's worth a shot. If successful, you'd avoid Thai immigration altogether.
I don't think they'd deny entry in your case. If there's any sign of trouble or if they start questioning you, show them your ticket out. They usually start with a question to establish the intended duration of your stay anyway.
Please report back how it went once you're through.