Way to undraw the bow without firing it

As of patch 1.04, as you found out, you can turn Weapon Taggingon/off in the settings, but not the minimap itself, or the radar function.

You can turn off the HUD completely, or turn some elements by applying some unsupported patches to your game. I know, this is not what you asked, but there seems no other way.

This guide explains how you can apply changes manually.

This forum thread lists some of these community patches. Beware, you might be kicked/banned from Multiplayer games if you play it with these on, so, make a backup of what you are overwriting.

UPDATE: The above mentioned patch files are apparently no longer hosted due-to copyright violations.

UPDATE 2: You can download the patch (for version 1.04) that removes the enemies from the mini-map here.

You really ought to be clearing radio towers; they reveal the minimap in the area, give you free guns, and provide a nearby respawn point (though you can't fast-travel to them). The latter benefit isn't that useful if you're on PC - even though it's not listed in the controls, F9 will quicksave and F11 will quickload, unless you're currently in a mission area in which case the game seems determined to become Call of Far Cry.

Clearing outposts is a take it or leave it sort of thing - as I'm sure you're aware, every cleared outpost becomes a fast travel location which can make getting around the island significantly easier, and provides you with an automated store for ammo refills. Some outposts have collectibles in them, if you're in to that sort of thing.

One less-obvious benefit of clearing outposts is that doing so usually unlocks some local quests. Normally, these are the "go here, stab man with knife" sort of things, or random local color; usually not the sort of thing that's gamebreaking to miss.

However, the big thing you're missing by not clearing outposts are the rare Path of the Hunter quests. A significant number of them have you hunt down rare, adjectival beasts that are impossible to find otherwise; those beasties are used to craft top-tier equipment like ammo pouches or loot rucksacks. If you want to have the biggest bags of all (and really, who doesn't?) you're going to need to clear outposts.

So, that being said, in your situation I would recommend the following:

1. Activate all radio towers, unless for some reason you object to seeing the minimap in which case you should become friends with quicksave/quickreload.
2. Use a list of Path of the Hunter quests to figure out which outposts to liberate; the ones for {adjective} {animal} are for rare animals you won't find outside of these quests (e.g, Black Panther, One-Horn Buffalo). Liberating these outposts should also give you a smattering of fast-travel points in useful areas on the northern island, though there aren't as many on the southern island so you'll probably want to grab a few extra there.