https://armyhistory.org/the-m28m29-davy-crockett-nuclear-wea...
https://en.wikipedia.org/wiki/Davy_Crockett_(nuclear_device)
At 1kt (max for the W54?) most of the effects are under 1 km: eg the radiation radius is only 0.84 km. Looks like if you shoot 1 mile away up wind, take cover from the flash, and then run away upwind you'd be fine with some hearing protection.
In this case I think firing the device upwind would be ill-advised, as then the fallout will be blowing back to you.
Edit: thank you for the correction @erikerikson! Noted, and best wishes!
Being upwind means the wind is blowing away from you towards your target and proceeds past your target further away from you.
https://www.quora.com/Would-the-Davy-Crockett-tactical-nucle...
Basically, even though the W54 had a max yield of a 1kt, the Davy Crockett used a warhead with a far lower yield, as low as 10 tons
How can I find out the degree and risk of radioactive fallout from a warhead equivalent to 2 - 10,000 tons of TNT?
Maybe don't fire on a windy day from downwind..