3 of my 4 chronographs use an optical system looking for the glint off the bullet as it pass over the sensor. The CED Millenium 2 Chronograph uses this principle:
https://www.midwayusa.com/product/101506602The sensors are available for replacement:
https://www.doublealpha.biz/us/ced-m2-replacement-sensorI don't know how much the OP can save on a $200 gadget if time has any value at all.
My Magnetospeed uses inductive pickups and is clamped to the barrel. Whether that changes point of impact very much will depend on the barrel. Who cares? I separate ballistics testing from zeroing - two entirely different things.
My next chronograph, if any, will be the Labradar because I can get downrange velocity. One thing is certain, the Magnetospeed means I don't have to hold up the entire firing line while I mess around getting the downrange screens adjusted. What a PITA! Not so much if you shoot by yourself, I suppose.
https://mylabradar.com/Coriolis can have a huge influence on point of impact, equivalent to perhaps 70 fps of velocity at 1000 yards depending on the round. Nearly 1 MOA in this video:
Velocity, by itself, is only a small part of the equation.
If you're looking for a great ballistics app, consider Strelok Pro
http://www.borisov.mobi/StrelokPro/android/See the last question on the home page regarding 'truing' where the muzzle velocity is back-calculated.