Typically, for a handheld that is wideband and prone to overload, a duck actually tuned to airband (and not just a claim!) can make quite a difference.
For airband monitoring with my handheld scanners, I use the antennas from my commercial airband transceivers as they are narrowband in nature as compared to the typical 2m/440 amateur ducks and whips. Depending on where you live, that can make all the difference. So instead of an 18" wideband whip, the 6 inch airband-tuned duck actually works better on a wideband handheld scanner.
One suitable combo is the Icom FA-B02AR airband duck, used along with the bnc/sma adapter that should have come with your 346xt. The Icom is bnc. You should have no trouble finding the FA-B02AR. Just don't let the tip touch your body as it will detune the antenna.
If you want a direct connect to SMA, then Yaesu makes a few airband ducks from their commercial airband transceiver line that would do just as well.
Some makers make the *claim* of being airband capable, when in fact they are just bog-standard 2-meter amateur antennas or actually tuned to the commercial vhf 150mhz band instead with a dinky little airplane icon stamped on them. Beware - they know you don't have the equipment to verify it.
I also second KA3JJZ's recommendation of trying a simple quarter wave ground plane first before springing for something commercial like the Centerfire.
22 inches of wire soldered to the center conductor of a bnc or S0-239 connector, and at least two radials (4 are better) of 22 inches soldered to the shell of those connectors and angled down just a little bit can do the job indoors. This is a very simple yet effective DIY airband quarter-wave groundplane.
