That's a lot of stuff to put into a 9v box. I'd look for something bigger. I have not seen a datasheet for that charger, either.
I don't know what the charger would do with up to 8.4v on it's output. I'd be surprised if any here did, as it's highly unusual to try that, and many may not want to even try to answer this because of that. For some reason, that compels me.
A charger should have a higher potential than the batteries, else I'd guess that the batteries could discharge to the charger. Personally, I wouldn't try it. I would advise getting 14500s or better and charge the batteries externally.
Someone else recently wanted to do this, and their design ideas had all sorts of problems with the batteries being in series and parallel at the same time, which is very bad. It looks as if you've figured out how to reconfigure the batteries using a DPDT switch. Looks like that can be done using 5 of the terminals, but that still leaves the charger problem.
That seems dangerous to me, as does the possibility of a slide switch making both circuits momentarily while transitioning between positions, causing the batteries to short-circuit. I would not trust the switch that much.
If I were to try such a thing (which I would not do,) I'd look for a 3P3T slide switch. The 3rd pole to disconnect and connect the the positive charger output to the circuit, and the 3rd throw as an 'off' position in between the 'charge' and 'vape' positions, hopefully minimizing the risk of making both contacts at once while switching. That center 'off' position would also be the 'kill switch' that is usually advisable to have, as well.
That's a bit complex, and any mistakes in that wiring could easily short-circuit the batteries and/or the charger. I'd probably also put fast-blow fuses on the possible short-circuit paths as well. It's an interesting problem, but it gives me the willies.
