The gun is the preferred method, IMO. If you have local experienced people especially. It’s devastatingly sad for you, whichever method is used, but that is not the important thing right now, what is important is what is best for the horse, and your sensibilities are secondary. You know that, obviously. If not using drugs to put the horse down, burial is more possible, since the body is not poisoned. Or, use as feed for carnivores, if that option is available. Use of a gun is far more environmentally friendly.
You know your horse, and have the best idea about what preparation may be the most useful to him. Even feeding some acepromazine may be helpful, calming, reduce any tension he may feel with a stranger coming around. The bucket of grain on the ground is the classic approach, but some people simply cradle the horse’s head gently with one arm, and place the gun accurately with the other hand. With your access to skilled people, they will have their preferences and usual routine. Consult the person you recruit in advance, so you know what to expect. Explain any of your horse’s idiosyncracies in advance that you feel may be a problem for the the person doing the job, if he’s head shy, or nervous of strangers etc.
It’s often not necessary for you to be present for this. Excess emotion on your part can be unsettling for your horse, the opposite of what you want for him. After working so hard to keep them alive for the extent of their lives, it is not necessary that you be present for their death, unless you want to be. Your call.
Sorry.