Is there a type of switch that is closer to a chiclet in terms of travel distance?

Kaihl choc switches (the V1 type) are going to have the shortest travel out of the keyboard switches that are common enough to use, and that's what most low-profile hobbyist mechanical boards out there use. There's a "choc amber" version that recently became available that have the shortest travel distance among choc switches (1mm actuation, 3mm overall), but they're pricey and I haven't seen anyone fill a keyboard with them yet. Those are also designed for fight pads, so I don't think they're made with silence in mind.

There are "silent" choc switches on their way (developed by Darryl lowprokb.ca), but they're not available quite yet.

There's also the Kaihl X switch with a 2mm overall travel distance, but they're also pricey and I think it next to impossible to get key caps for them (at least it was last time I checked). Hazel is the only person I've seen make a keyboard for those: https://github.com/hazels-garage/shortstack. Awesome stuff, but probably not easily obtainable.

I've achieved something similar with MX Ergo Clear along with G20 keycaps and o-rings. The switches have a much more similar tactile bump to laptop switches, the G20 keycaps lower the overall height and make the keyboard nearly flat, finally the o-rings shorten the travel to just under 3mm. DSA keycaps are the same height too but have sculpted surfaces.

It would be remiss of me not to mention that choc minis exist (pg1350) they have slightly less travel than choc v1 but are less common, but they use the same keycaps. I think there is a corne version somewhere (that I made) that uses them. I like choc minis a lot, but they have a bad reputation for price/consistency.