That'll be a dumb trickle charger, right? Be careful that you don't over-charge the battery. It'll be 500 mAh, so if the charger is rated at (e.g.) 500mA, it'll charge it from flat to full in 1 hour. If it's 1000 mA / 1A, it'll do it in 30 minutes, and so on. Don't leave it plugged in for hours, or overnight.
You're planning to get an AEG, right? If you use a Nimh battery in that and get an auto-cut-off Nihm charger for it (and you definitely should), you can modify your pistol battery to use the same charger.
Buy a spare connector that matches whatever the AEG battery uses (mini-Tamiya, Deans), cut the pistol charger cable near the wall-plug end, then wire your connector onto the cable. Use a multimeter to find out which wire is +ve and which is -ve although (don't quote me) I believe the wire with a grey stripe is the +ve.
It sounds more complicated than it is, it's just clip, strip, test, crimp, and then throw that trickle charger in the bin where it belongs.
My bad, I missed that you were going sniper. Well, maybe not worth buying a cut-off charger and modifying the AEP holder, but do be careful about over-charging it.
Cheap cheap gun torches are problematical. I've already sent a couple back to Amazon for not actually being usable. Avoid the "5 mode" ones like the plague - they all seem to cycle through the modes every time they're switched off and on, so you can't just leave them set to high or strobe where you'd want them.
Amazon at least has reviews and gives the opportunity to ask questions, but every answer that I got for multi-mode torches was "cycles through the modes".
They pretty much all make ludicrous claims about their light output as well, and chop and change functionality without changing the listing.
The cheapest way to do it is to buy a 25mm RIS rail mount for a few £££ and a simple on-off 25mm diameter LED torch for about the same, rather than buying a specific "gun torch". You can get gun torches that come with pressure switches torches, or buy separate pressure switch caps for specific brands (of which your cheap one may be a compatible knock off), but they're commonly flagged as fragile. Mine gave up after one game and I had to go in with a drill and soldering iron to rescue it, so if you want to avoid surprises and hassle at a low budget, keep it simple. One mode, push button to switch on and off, assume that anything under a tenner will produce more like 50 lumens than the multiple hundreds that they all claim.
Best of luck - if you do find a good 'un, please sing out.
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