The old superstition of giving a knife. It severs the relationship. Attach a coin to the knife to be immediately returned to you. Thus the knife was paid for and the bond is not cut.
"That's true, I never give anyone a knife, they pay me a quarter. Friendship last forever."
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^^So true or not, the price has gone up. A friend gave me a Puma when I left town decades ago, and asked for a nickle back. I did see him many years later when I moved back to the state and we kept in touch thereafter
This has been an interesting thread since I was not looking for a new knife. But to provide any useful modern input I looked at many that have been suggested. Ironically a couple Puma knives appear to almost fit my personal, very picky criteria for a sheath hunting knife, though nothing in current offerings would replace my nearly antique Gerber A450 knives. The illustration below is not of my well-used knife, but of one for sale at a collector price on the net.
Knives can be very personal items, and indeed, after field dressing, skinning, boning, and butchering around a couple hundred large game animals now, I have some personal preferences. I find that a 4 to 4.5 inch blade is quite sufficient for anything up to the size of a bison, and safer than a big pig-sticker. I also like a blade with a little flex because I bone out practically everything, because I also pack it out on my back. The flex follows the bones easier and gets more meat on the first cuts. I also like a somewhat slab-sided handle, rather than round, because I like to know exactly where that edge and point are aiming relative to my other hand that may be shoulder-deep inside a chest cavity. I don't like cutting myself. That also applies to having the handle and blade along a single plane so the edge and point are not up or or down from the handle position. I only use replaceable blades in my skinning scalpels for fine work. Tried the replaceable blade knives, and don't like them myself. I also have no interest of having a super sharp blade break off in my work where I cannot see it. Maybe I am just paranoid from having scalpels do that regularly.
A general field dressing and boning blade is not the best as a skinning blade, but you can get the job done. Conversely, a big-bellied skinning blade is cumbersome for dressing, boning, and butchering, but great for skinning.
Small Lady, a number of the suggested knives top out over your stated budget, including the one Benchmade fixed blade I would have suggested - the Raghorn - but that handle might be a little round. The pricepoint cuts it out. On the other hand, you did say "not folder", but the Benchmade folder that you might consider anyway is the Griptilian drop point. Good blade shape, very useful quality knife, good warrantee. I have 2, and always have one in my pocket. It serves as a second knife when I am hunting, in case the Gerber dulls before I can sharpen it.
The Pumas I might suggest are the Catamount, which has an attractive wood handle:
And the Puma Dexter, which has a much more practical Micarta handle, this knife has a slightly thinner blade, and might flex a little:
The photo below is of a generic Gerber A450 - no longer made, and expensive on the resale market.