If you're thinking in terms of something like a Hukka, as mentioned, you could use an SLA (sealed lead acid) battery for the part that sits on the table. They aren't terribly expensive and are much safer than any Li-Ion cell. The big disadvantage with SLA batts is the size and weight. Something like
like this would do the job nicely. Chargers are inexpensive and readily available. Just use 4 switching regulators for people to control voltage at each station. You'd have to use a switching regulator over a linear regulator due to the fairly large drop in voltage you need.
If size is an issue, a stacked LiPo for hobby applications
like this could power 4 atomizers for some time without hardly loading it. However, LiPos are the most volatile of all the Li-Ion types and you absolutely need to protect them from electrical shorts. A PTC fuse is an easy and reliable way to do that. You can charge it with a balancing charger in a safe area to mitigate the charging risks.
The problem with using LiCo cells like 18650s or 26650s is they have the lowest max drain and charge rate. Hence, they require the best protection. That's why a protection board is typically used with them. The Hobby LiPo I linked has a max drain of 100A. A PTC fuse or even a slo-blo fuse is perfectly adequate to protect one from shorts since those batteries can deliver quite a bit of current before any damage occurs. The same can be said pretty much for the IMR round cells which can also deliver a lot more current, but they do it at the cost of charge capacity.
You need to protect any battery you use from over-discharge. Even the SLA ones get damaged from that. Just add a simple voltmeter like the ones you get from MadVapes to monitor battery voltage. SLA batts are min 10.5V and Li-Ions are min 3.2V per cell (except the LiFePO4 ones which you wouldn't use for this).
Optionally, if it doesn't have to be portable, you could do a plug-in-the-wall setup with a high output 9V or 12V power supply. They are readily available. They're typically used for laptop computers. The one for my laptop puts out 200W. With a switching regulator at each station (doesn't waste power), you could provide each person with as much as 3A@6V (72W total) and it would still be well under the max output for the power adapter.
I'm sure there's other ways to go about doing what you want as well, but what I mentioned is what comes to mind right away.
