I use Track's Mink Oil or Neetsfoot Oil for patch lube for hunting, from .32 to .69 cals.
Melt the Mink Oil, doesn't take much heat, soak it up into precut patches, then squeeze out the excess back into the tin.

For Neetsfoot oil, simply soak the pre-cut patches in the oil, squeeze out the excess.

I put pre-lubed patches in a tin, like Sucrets tin, or a plastic Speer box.

In the larger calibres, say .58 on up, paper ctgs. work well for hunting. The ball and paper thickness must give a tight fit into the bore. The wadded up paper beneath the ctg. helps seal the pressure and flame behind. No fires (with my combo) and accurate shooting, whether WW balls or pure lead.
With my .69, I can fire 10 accurate paper ctg.s (match patched ball accuracy) before the fouling gets bad. That was with 165gr. 2f charges. I then load up 82gr. (3drams) with a sopping wet spit patched round ball and fire that. That cleans the bore, ready to fire another 10 ctgs.

A loading block can be used for lubed, patched balls for hunting. The one I have holds 3 shots, thus 4 with the bore already loaded. I have left a Neetsfoot Oiled patched ball loaded for 5 months, then when firing it off, it hit centre at 100 yards, just the way is was supposed to. This was a test I did back in about 1989/1990. I loaded the rifle Sept 15th or so, then didn't get to shoot a moose with it that fall and fired it off around the end of February. We went out to the range just to try it out. After that shot, I tried 10 paper ctgs. - perfect shooting results. Good stuff.

Now, for big game hunting I prefer to load the rifle with an oiled patched round ball, then stick 1/2 dozen paper ctgs. in my pocket with a round capper 'disk' around my neck and off I go. I may or may not put a starter in my parka pocket.

For bunnies with my little Mtn. Rifle flinter, I use a possible's bag and tin of oil lubed patches. It likes Track's Mink Oil and the second and 50th shot goes down easier than the first one. No wiping needed.
.350" round ball and .022" denim patch. Loads easy and actually no starter is needed but I use one. A choked up rod, 1/2" showing below your hand can even start this combination into the bore as the tiny ball is easily formed into the bore. there is not a lot of lead to move. The larger the bore is, the harder this becomes without a starter. It's very accurate, very clean and fast shooting.

For that sort of shooting I wear a possibles bag, main powder horn and carry a priming horn, patch knife, loading block or loose balls in the pouch, lubed patches. In the left side pouch I have a bit of excess patch and a cleaning material strips, tools (screw-driver knapping hammer)jag, ball screw, spare flints and a sandwich & of course the camera.
So - horn, priming horn and possibles on right side, bag with accessories and lunch, left side.

Edited - should have noted - if you use a loading block made of wood, it should be finished inside with a water proof finish, just about like a rifle's stock. If not, the block's wood will absorb the oil from the patch.

Cutting boards, HDPE or UHMW are excellent for making hunting loading blocks. You do need one thick enough for your ball & patch - ie: 1/2" to 5/8" or just over for 50's to 62's, 3/4" for your 12, etc. Bore the holes so the patched ball is quite a snug fit, then use a small square file to file some 'grooves (4)' around the interior holes, to reduce the friction and contact surfaces. I found this to work very well with my own loading blocks. In the small calibres, like .32 and .36/.40, a 1/2" thick old (or new) cutting board works very well, for 10 to 20 shots if you are in a target rich environment, like shooting gophers.

Do NOT use a water based lube or a water mixing lube for hunting. I put Ballistol in this same category as it will/can absorb moisture - thus it is not going into my rifle bores.