Snap-On 9/32-inch drive and 1/4-inch drive pieces had different model numbers. The 9/32-inch drive pieces will all be marked M-***. The 1/4-inch drive pieces will all be marked TM-***, except for the ratchet, which is GM-. The Snap-On 1/4-inch drive sets, introduced during WWII, did not come with a tee-handle (with a continuous looping T). I'm not sure any mfgr's 1/4-inch drive sets did. That style handle was pretty much phased out by the late 1930's, also when most mfgrs phased out 9/32-inch drive in favor for the 1/4-inch drive size quickly emerging as the industry standard. Snap-On, Plomb, Armstrong and Williams continued making 9/32-inch tools throughout the war - in support of USAAF use, but by the late 40's, it was obsolete.
If you intend to actually use your tee-handle, rather than treat it as a collectible, you could carefully grind or file it down 1/64" on all sides of the drive stud, effectively reducing it by 1/32" in diameter to 8/32" or 1/4". Wouldn't be the first time. It was quite commonly (and usually quite crudely) done on 9/32-inch drive tools in the late 1940's. And more often than not when you find an orphan tool marked with a 9/32-inch drive model number, it's just as likely to be grinded down to 1/4-inch. Not to be judgmental, but I would recommend finding a nice vintage 1/4-inch hinge handle instead, with a hole for a tommy bar, and leave the Snap-On 9/32-inch tee handle alone. Someone could probably use it to complete a set.
EDIT: You may run into other 9/32-inch drive tools, including Plomb, Williams, and Armstrong, maybe others. But no, it's not nearly as common as finding 1/4-inch drive.