What is the weapon light? The blue rechargeable batteries work perfectly and are very inexpensive. However when you are running two of them you can run in to problems with back charging. If the light is LED you can buy an inexpensive pack, it is basically 2 CR123A cells in one package and you bypass the the problems.
I have been using both single and double rechargeable cells for years, used daily and charged daily with no issues.
If your flashlight uses a bulb then you will not be able to use the rechargeable cells, they deliver more current than primaries and will instantly kill the bulb.
The Battery Station house brand are as good as any other when it comes to running a flashlight, they are $2 on the site, and can be had even cheaper by using a code on the website.
The Lithium found in those batteries (any CR123A) is great stuff, but when it comes to rechargeables they use Lithium-ion, even better stuff when it comes to cold weather use.
In this photo you can see the blue rechargeable 123A, and beside them are the double units I was talking about, they are made for 2 cell applications like yours. They come in two flavors, protected and non-protected, do not buy unprotected cells!
PM me if you want more info, like where to get them.. Have your flashlight model handy though.