I very much doubt that they do it in the exact methodology I described but I assure you that market participants do this.
There is probably published material available on 70's and 80's hedging techniques but now that they are known the market converges. The problem with what you're asking now is that anyone privy to modern strategies would be sued out of existence for divulging them. A successful hedging strategy is very much classified as a trade secret.
The only thing of value a hedge fund provides, if it does indeed provide any value, is it's investment strategy. There are no perfect hedges because they'll typically be arbitraged out of existence but the logic that goes into hedging is the reason liquidity preferences exist now.
The finance industry has a wholly different outlook on things than normal people so I understand the confusion here, it took me a bit to fully grasp why and how to do things even once I was immersed in the industry.
Also, I should emphasize here: the theory behind the concept looks pretty but in application the assumptions can completely obliterate the success of the investment. The book "A Random Walk Down Wall Street" by Burton Malkiel covers a lot of the finance industry from an academically rational perspective.
If you read that book you'll take away the counter point to everything I've said here. Which is, there is no evidence in advance that a hedge fund can successfully hedge. After the fact, survivor bias may mislead us into believing that what appeared to be a sound strategy may have just been luck.
At the end, the challenges to hedging aren't obtaining the appropriate instruments or taking on the risk, these are problems that all major financial entities are comfortable dealing with. The challenge in hedging is that you don't know how accurate your assumptions are until the hedge is complete.
Essentially when crafting a hedge you are playing a binary scenario (A wins and B fails, or A fails and B wins). The problem is that the input assumptions also need to hedged, and then you have assumptions on those hedges, and so on.