I've been using a WW II trench shovel for 20 yrs ln local parks, on a local college campus, and a few H S campuses......no troubles IF you fill the holes and then dress the area.
Just a little garden digger for hunting around the public. Keep it low profile, you don't want to come across like your about to start diggin' graves or tearin' the whole lawn up. Out on remote sites pull shovels and diggin' picks out.
My expereince has been that walking around with a shovel will attract more negative attention than a trowel will, even if you dig cleaner with a shovel.
Most hunters I know of don't use shovels in public areas for that very reason.
I think it was $15 when I bought it, but serrated edge help cut a cleaner plug, deals with small roots. and measurments on it for knowing how deep you are....
Okay it's all theory because I am still new at any of this, but a pretty good theory darn it!
Never use any type of "shovel" in a park! Whether you can cut clean plugs or not, it draws to much negative attention and puts all detectorists in a light of "tearing up" public grounds. Hand trowels and towels to keep it clean!