Sorry to be slow seeing this.
When you say face paint, are you looking to do tattoos, warpaint or both?
For red tattoos, I use a maybelline lip liner pencil https://www.amazon.co.uk/Maybelline-Color-Sensational-Liner-Hollywood/dp/B0079Z4JE2 - I find one application lasts me the weekend despite being a heavy sweating type. It’s a little faded on Sunday but I think that’s largely because I wake up with copies of my binding of thorns transferred onto my forearms each morning!
My character also has blue tattoos, for which I use a couple of liquid eyeliner pens. They have a fine tip that’s half way between a brush and a felt tip pen. I think they are maybelline too but I can’t swear to it and am not in a position to check. I don’t think any of them cost me as much as a cake of snazz and are easier to have in my bag in case I do need to make emergency repairs in a toilet block.
Assuming that you aren’t in the Navarr facebook group, there have been discussions about this now and again. For a quick and dirty summary, transfer printer paper gets recommended often, for both laser and inkjet, along with temporary tattoo inks and alcohol-based paints (the advantage there being that snazaroo warpaint can be rinsed off without affecting the tattoo work). People have also recommended a mix of prosthetic adhesive and acrylic paint (commonly referred to as “pax”), a variety of waterproof liquid eyeliners, greasepaint, sharpie pens and a website that sells temporary tattoos. Many also recommend using a fixing powder/spray or hair spray to seal any paint and make it last longer, not tried it myself but probably should.
A trick attributed to the imperial orcs is to wet snazz with fixing spray instead of water, apply as normal and then spray over it again once dry.
Things specifically mentioned to avoid are Citadel acrylic paints (and probably any other brand meant for toy soldiers) and semi-permanent hair dye.
While I don’t have links for most, the following brands get recommended, which I’ve broken down by type below.
Alcohol-based: Temptu Pro Dura (liquid); Mr Dashbo.
Print-at-home tattoo paper: Silhouette Temporary Tattoo Paper https://www.amazon.co.uk/Silhouettes-MEDIA-TATTOO-Silhouette-Temporary-Tattoo/dp/B0043WJ3OA
Ready-made tattoo transfers: www.tattooforaweek.com
Temporary tattoo ink: Colorini; Stargazer tattoo pens; Ladot Ink
Waterproof liquid eyeliner: https://www.ebay.co.uk/p/1581885613?iid=323808298413
Hope some/any of that is useful!