This is an unknown area for me so I'm just asking, but with a bit of knowledge on the ballistics side.
From time to time I read of people acquiring pistols for close range humane dispatch. IIUC, this is pertinent to a deer that has been shot and not killed, often in cover or an unsafe position to use a full power round. I have often made use of downloaded rounds in centre fire rifles. By way of illustration, I have downloaded all of the following calibres. .223, .308, 30-06, 7.5x55, 6.5x55. My preferred powder is 'Unique' and the load varies from about 7 grains to 20 grains. Especially if using a lightweight bullet the effect is such that shooting, for example, a 30-06 feels and sounds like shooting a .22 rifle.
I believe that the police are often reluctant to permit such a pistol to the casual deer shooter so if there is no pistol and such a situation arises, what is there to do? It has occurred to me that, to use a .308 as an example, a few rounds of such handloads would serve well for this purpose. As an example, the Hornady 100 grain semi jacketed bullet would appear ideal if placed in front of about 7 grains of Unique would provide a relatively low powered round for close quarters dispatch of a wounded deer with minimal ricochet hazard, given the circumstances. This round would be easily identified by feel alone (And of course, the shooter could also look at it before loading!) so not mistaken for a full load.
For anyone unfamiliar with downloading handloads and who fears bad things happening I have researched this to hell and back and if done properly, i.e. with fast powders (It's the slow powders that detonate and blow up rifles) it is perfectly safe.
Please bear in mind the first line of this post.