I got a tárogató maybe 2 or 3 months ago. It's a good horn; a Hungarian folk instrument with a timbre somewhere between a soprano saxophone and a clarinet with a chest cold.
There's not a lot of english-language info on it, and I intend to write some more since it is desperately needed. I don't know that much about it yet, though. What I do know is this:
Don't swab it out, especially with a clarinet swab! It's conical bore and impossibly narrow in the top joint! You'll get it stuck!
It took me a sweaty 45 minutes to carefully work the packed swab back out the way it came with soft hammer taps on a cleaning rod I requisitioned from my valve trombone case placed up against the jammed cloth, then completing the job with needle-nose pliers to fully take it out. I could've really damaged a valuable antique.
Clean the pads some other way, English-reading audience! Not worth it. Keep your swabs out of the tárogató's narrow body.