It sounds like you don't need to keep these values in a file at all then, you have a few other options. Saving the json response to file might still be your best option, but these are worth considering.
1. Use hash tables. Parse all values for fastest lookup later. This is closest to your INI storage, and can even be saved to INI if you want to persist when mIRC is closed.
/hadd weapon.stats Kar98.Kills 300
/hadd weapon stats Kar98.Accuracy 45
var %Kar98.Kills = $hget(weapon.stats,Kar98.Kills)
2. Save json to binvar. I'm not sure exactly how much faster this would be than using a file.
var %bvar = $json(%ref).HttpBodyToBvar
hadd -mb cod.responses stats %bvar
var %bvar = $hget(cod.responses,stats)
/JSONOpen -bd cod.response.stats %bvar
var %Kar98.Kills = $json(cod.response.stats,data,lifetime,...)
3. Don't close the json handle until you replace it. Whenever /JSONOpen is called currently the -d switch is used. Remove that, and either open it with a custom %ref name or save the returned %ref for later. Then you just access with $json(%ref,data,lifetime,stats,...) later on without having to request from the API again. You can /JSONClose on a timer to remove it later then refresh stats. Could be adding unnecessary complexity.