Go cheap, get earbuds.

Avoid anything listed as an IEM (in ear monitor), or that has tips that fit into the ear canal.

Sony makes some decent ones that stay in place well, for ten bucks or so. Less if you don’t want/need a mic.

You’ll still get directionality.

Barring that, you’d want to go with something on ear as opposed to over ear. Usually, the type that sits on your ear rather than having big cups that cover the ear will have less perceived bass because of the decreased seal.

Otherwise, you’re kinda SOL. Most of the “gaming” headsets are meant to be partially noise isolating via encircling the ears fairly consistently, so even gear that has less bass response in the hardware itself still move the air inside the cans in a way that’s pretty perceptible compared to anything else.

Logitech used to be reliable for quality (overall, wouldn’t meet most music standards), with the h390 being a decently low bass option. Sennheiser makes the PC series (they have number versions) that are acceptable durability, with clear sound for environmental effects at a range of price points. Beyerdynamic has the mmx100 that are relatively low bass response, and don’t seal so tightly that it becomes over present.

If he wanted a separate mic, something like the koss portapro are wearable for hours, and aren’t too bass heavy.

But, and this is vital, when someone has a very specific use case like this, they’ll need to try multiple things and keep what’s best. Nobody can promise that any headset/headphones are going to be right for this. It’s impossible, literally impossible, to have zero bass production in the drivers because that’s all in the sound source. The best you can do is picking gear that has a higher cutoff for the low frequencies and doesn’t reproduce the bass as prominently. Having less of a seal to the ear helps drop perceived bass, but can’t entirely eliminate it.

To entirely eliminate any frequencies that would be considered bass by most people, say anything under 100hz, you need to have hardware that filters it, and you don’t get that kind of hardware in a headset; that’s done either by the hardware on device, or by the software that’s handling the sound. And, an equalizer can only go so far in that regard. It would help, yeah, but it isn’t going to remove every bit of bass.

As a side note, I get it. If you’re gaming heavily, booms can be fatigueing even more than the higher pitches (though that changes the higher you get).