If I was after dangerous game, going into the thick stuff, I would be carrying a double rifle in hand with a cartridge capable of taking the fight out of a big dangerous animal. Rifle would not have a sling - they just get caught.
This is how many many professional African Hunters do it. African Jesse bush and elephant grass are very thick. You want a fast handling rifle that carries the energy to put things down.
470 Nitro Express - a 500 grain bullet @ 5,000 plus ft lbs of Muzzle Energy
44 Magnum - 300 grain bullet @ 1,500 ft lbs ME
243 Win - 100 gn Bullet @ 1,800 ft lbs
Pistols might be handy and are better than nothing, but when your life depends a proper rifle is so so much better.