That would be The Question!
My contacts (both for distance vision) prevent me from seeing well up close. So do my glasses for that matter. Never bothered me for shooting peep & pin, but I do it "all wrong" according to many (including a guy who said he was a serious champion competitive pistol shooter, if you're willing to accept an Internet claim)...
Anyway, when I shoot irons, I check their alignment and then shift my focus to the target. With a peep, I just floated the fuzzy dot into position over the target. A guy who went by Rattus used to say that center fuzzy is the same as center sharp - and my shooting never could have disproved that.
So now I would recommend keeping a pair of cheaters handy and keeping the target in focus for both eyeballs. YMMV.
I guess I'm used to being one of the kids over on the Wall, but I rolled over 50 a few years ago and I can see clearly at arms' length without glasses, or I can see the rest of the world!
I do use the "monovision" method spoken of above, and use a contact that is underpowered by about one full diopter in my right eye, which brings the ppin into perfect focus. You can shoot decently with a fuzzy blob out there where the pin should be, but the aim will not be as precise, nor will that fuzzy blob remain visible in the low light of early mornings and late evenings when most of the action gets going.
The choice is not between a fuzzy pin and an equally fuzzy target. It's between a fuzzy blob that may become completely invisible in lower light, and a target that's still visible and in sharp focus with both eyes open and slightly out of focus when you shut the other eye for final aim. You can check out the difference easily by just looking through a pair of reading glasses. The ones that bring small print into sharp focus at arm's length will also bring your pins into sharp focus. Take them outside and see just how little they hurt your vision of something a block away. And remember, your other eyes will still be corrected for full distance vision or very nearly so, and will feed your brain the best image while you have both eyes open.
Kind of surprised to see so many say they had trouble with the monovision method, as it worked great for me and the few other guys I've discussed it with.I've known bowlers and golfers who both used contacts that way and liked them, enjoying the ability to see the pins clearly and also the scorecards, especially when they were doing the scorekeeping.
Some guys found them slightly distracting if used all the time, but I like them for all-around use. Driving, I can see the dashboard numbers and symbols just fine and still see the road ahead and read distant signs clearly without having to change glasses or tilt my head back to use bifocals. When I first got some contacts that were made that way, I figured I'd just be using the for golf or archery, and ordered extra lenses for the right eye that were also fully corrected for distance vision. I soon discovered that I preferred the monovison method for regular daily chores as well as for shooting, just for the convenience of always having one eye already equipped with a "reading glass" so I didn't need to fish readers out of a pocket to read a label or the menu. I had read that there were some folks who had problems tolerating the differing focal lengths, or adapting to them, but to me the transition was immediate and completely without bother.
Haven't been in a Holiday Inn lately, but I'd say the best bet would be to at least give the method a try. Usually the vendor of the lenses will bee glad to furnish you a couple with a bit less correction as a trial fit. A couple days should be enough to tell if you'll like them that way or need the same amount of vision correction in both eyes. If it works for you, I bet you'll really like it, and if it doesn't you're only out a few lenses and you'll know that method isn't for you.
When I had my lasik surgery - I had my right eye set up for close viewing and my left eye for distance. Never had a problem.