To put this in perspective... A dog can smell about 44 times better than a human. A deer can smell about 60 times better than a human and about 35% better than a dog.
No matter what your cleaning regimen is, your firearm is still going to have a hint of odor associated with it. Be it from the cleaning products you use, your ammunition, the oils from your skin, etc... Scent eliminators have their place, but they also have their limitations. Scent control is dependent on too many factors to actually be controlled... Especially if we consider the olfactory senses of the critters we hunt. What is a faint whiff to us, can be a stink bomb to them.
If you want to hunt the wind, even in areas where the air is moving too slowly to detect, take along a bottle of detector. I use an old visine bottle filled with powdered mica. If I am unsure of the wind, I shake the bottle, remove the cap, hold it at arms length, and give it enough of a squeeze to get a puff of the mica. It tells me exactly which way the air is moving, how fast, and which direction I need to focus on moving in.
In the thicker woods, with rolling country, the prevailing wind may or may not impact us much. The thermals, upslopes in the mornings, and downslopes in the evening are common during the warmer weather, but in the winter time, when temps are typically colder, the thermals have only limited effect and only very locally, but synoptic conditions (the locations of high and low pressure cells) have a more pronounced effect in air movement... During the winter, the thermals may only have an influece within a north-south draw with an east facing slope that takes sun in the morning, but the synoptic effect will shift that upslope movement to a north or south westerly depending on the barometric pressures... In this instance, I would plan on hunting into a quartering wind... And, I still have my little bottle of detector to confirm what I need to do.
It works in the deep woods, it works on the prairie, it works during blizzards, and it works during rainstorms... Learn to hunt the wind.