Unfortunately, no you can't. Followers will always choose the "best" weapon available* as defined by the monetary value of the item: expensive but cursed weapons, for example, will take preference over more reliable ones. (The only exception may be tech items in the hands of high-MA followers; I've never actually tested this.) I believe they'll even unequip a shield or lantern in order to use a two-handed weapon, and ignore obvious penalties such as not having the necessary MSR (minimum strength required).

This is one of the most annoying things about followers, IMO. But I can see where the developers thought this would be a good idea: in the heat of the battle, do you really want to have to stop and tell Virgil to switch to the damned axe? (This is presuming you even let your followers fight — which, as an XP hog, I almost never do anyway.)

The "auto switch weapon" option only applies to your own PC: if you run out of bullets or arrows, for example, the game would switch you to the best of your available melee weapons. (Again, defined by monetary value; which means it'll choose that so-so Caledonian longsword over that super-fast katana.)

*Armor too, providing it's the right size for them to wear. Rather than treating followers like pack animals, the game assumes you wouldn't give items to them unless you wanted 'em to be used.