If you know that your gauge is "more picky" than your tightest barrel, then I can see the motivation for taking the gauge with you when buying ammo locally. Speaking as one who has pulled out a barrel in a gun store and gotten those VERY strange looks from the guy across the counter, I can understand.
[And I will tell you that I do not buy a lot of case or cartridge gauges. I'm still using a nice, steel, single-hole gauge from Midway purchased about 1990 ! I keep it lubed with sizing wax that so far has kept all the corrosion away. ]
What a gauge will tell you is about the physical dimensions of the case.... the decreasing diameters along the tapered case body and the concentricity. It will also find distortions along the rim due to rough handling by the extractor. It will tell you if the bullet is seated co-axial with the case, and it may tell you if your cartridge is too long to fit the mag. (That is to say, if it exceeds the SAAMI max length of 1.169".) But, the gauge does not tell you anything about the freebore and the bullet clearance to the rifling.
For that one single measurement, you need the barrel. Only the CZ barrel has the rifling in position to tell you about the OAL. So I would take the barrel with you and do the "Plunk & Spin". If this is a pain, then take it once and try every cartridge type/ style/ brand in the store... and record the PN's of the ones that will work on a note pad or with your camera. That way you have the manufacturer's PN and can build a data base of ammo that works for YOU.
Once you know what brands are OK, you can buy without any gauging. And, if you're reloading and doing the Push Test, then you can use your gauge with confidence, knowing that the OAL is good to go.
Newer gauges may give the user more information. I admit, I'm old and my old processes are built around my old tool set. What do you see ?