A chronograph is 100% unnecessary. Determining what load is safe is what manuals are for.
I used to have a chronograph, I think I still do, but I haven't used it in decades.
Back when I was using one, in the prehistoric, pre-Internet days, I shot a lot of different loads in quite a few calibers, and comparing the numbers I got against what was in the published manuals taught me something.
It taught me that my loads were all delivering exactly what the books said they would,
allowing for the expected variations because I was using my guns, not the guns they used for their testing.
If the books says barrel length X load xyz = 2987fps. You shoot the exact same load (as close as you can get) in a rifle with the same barrel length, and you get 2923fps on your chronograph. You shoot the same ammo in a different rifle with the same barrel length and get 3026fps.
THEY ARE ALL CORRECT.
The manuals won't tell you what is safe in your rifle. The tell you what was safe in the test gun(s) they used, and there is a really high probability that will also be safe in your gun, but its not a 100% guarantee, which is why the manuals are GUIDELINES, and careful load testing and workup in necessary and important.
Everything has a range of tolerances, and when they line up just the right way, you end up with results on either end of the bell curve, instead of in the middle.
There are guns that show pressure signs (sticky extraction, flattened primers, etc.,) at or sometimes even below the listed starting loads. Some will do it with factory ammo.
There are also guns that can shoot loads well above the listed "maximums" with no observable pressure signs or ill effects.
Any combination of things is possible, and it is prudent to proceed assuming a worst case, until your testing shows you otherwise.