I keep an Excel spreadsheet of all the guns I have, when acquired, and what I paid for them. Also the serial numbers. I have photographs of all of them in separate electronic files. It's not hard to do if you just acquire guns and only occasionally sell them. If you're more active in buying and selling then it gets longer. It's sort of like a stock broker's tradings blotter. I periodically update it with what I think are current values (according to the auction sites). I also keep a running inventory (on a different page of the spread sheet) of my ammunition supplies, reloading dies etc for each caliber. I don't list what I've paid for that stuff, because it would be too complicated, changes too often, and too much work to do all the addition and subtraction. I'm OCD about having buckets full of empty brass laying around (I'm compulsive about picking it up when I can find it) as well as components to load it, so I periodically go on a bender and reload for a month. When I found out I had 9000 rounds of loaded 30-`06 and at best shoot 60 rounds a year, that told me I had to STOP reloading it despite the temptation to do so.
It's a "for me to know" sort of thing, but I've also told her that it exists. I've told my brother too (but he hasn't seen it), so he could help her with it in the event of my passing. It's purely a personal thing.
But the general premise is that if that sort of thing is 1%-5% of your total estate value, $25,000 total value, or less than 30 guns it's not a big deal. If it's greater than 10% of the estate, $50,000 in value, or more than 50 guns, that's getting in to the realm of where heirs can really squabble and destroy their relationship, particularly if one is in to that sort of thing and the other is not. The above numbers are totally arbitrary. You have to decide where the line is.
I'm going through that very situation right now concerning the administration. of my father-in-law's estate (former police chief). In his case there were only a couple of guns, but his big passion was collecting stamps---45 albums full of them, (not just U.S., but many foreign collections) and he inherited his father's, and grandfather's collection that was started in the 19th century. I'm not particularly in to stamps, but find them interesting. My wife wants to preserve the collection intact as a family legacy item. It would be close to impossible to do a detailed inventory and appraisal of what is probably 300,000 individual stamps. The entire collection would probably appraise at $10,000-$13,000. Unfortunately, he did not leave instructions in his estate directives as to how to deal with it. My wife well understands there are huge bid-ask spreads in that sort of thing, and they (generally) trade at severe discounts to the Scott Catalog value. Unfortunately her sibling is someone that doesn't understand that concept. He doesn't want the stamps. Only money. He just looks at the catalog and wants to be paid that much as a compensatory distributional offset. (He doesn't even understand that concept that it would be proportionally ratable.)
So write it down, and leave instructions. Keep the file hidden if you want, but leave instructions on where to find it. Just the stuff you have. If you want to keep a book on what you've spent, that's up to you. It can't hurt, and may provide you a form of discipline if you need some form of self-restraint from time to time---and we all do. It's pretty easy when money is ample to justify a purchase by saying ; "it's only XXX dollars".