I haven't used this mosquito sniper thing but I have been using a battery powered sprayer for about 3 years now and I love this thing. I get very consistent applications provided I can walk backwards consistently.
I use that for herbicide and insecticide and I have a smaller hand pump tank that I use for spot treating with Roundup.
OK... so this page on Amazon has an answered question about the battery on a similar sprayer https://www.amazon.com/Scotts-190567-Lithium-Ion-Battery-Technology/dp/B07NNWK7CT?th=1
and the answer is it's just two standard 3.7v 18650 batteries. So that makes it easier to guess.
Now.. THIS page has a question about the charger for a pump that LOOKS like the same one: https://www.amazon.com/ask/questions/Tx10JP79IYIT9C6/ref=ask_ql_ql_al_hza
The answer is "9v 15Watt charger"
Which gets us to here: https://www.amazon.com/SoulBay-Universal-Switching-Interchangeable-Electronics/dp/B0722WN5TG
With multiple barrel sizes to help match the plug size even!
Its easy to do and they dont recommend to use is on a hose end sprayer. Granular or the WDG powder is the way. If you go with the WDG, get the Ortho battery sprayer here:
Just section your areas off to 1000sqft sections and spray that one gallon over that area.
You can get the small bottle which is like 25$ and I think give you 6 applications. Thats TWO applications ( early and late spring ) at 5.3g each and one in the fall at 13g. The smaller bottle is 141.75g and the yearly application above equals to 26g.
Again those are per 1000 sqft. So if your lawn is 5000sqft, you'll use 26.5g NOW, another 26.5g late spring and 65g fall time. Thats 91g roughly a year.