Making my own waterproof battery pack?
For the batteries, what really matters is mostly voltage rating (7.4V).  Any bettery with the same voltage should be compatible with your light.  The mAh rating in simple terms indicates the "duration" of your battery pack.  The larger this value, the longer your light will last without a recharge.

You may or may not be able to use your original charger depending on the replacement battery you expect to use.  We need to known your replacement battery to help you out with this: your lithium ion charger will most likely only charge safely lithium ion batteries with same cell setup.

For the packaging, a small plastic electronics case may do the trick.  Use some exterior silicon compound to fill the holes so that the water do not enter in the package.  You may decide to change your connector to something more waterproof.  A cheap waterproof connector may be a connector from an old car scavenged from a scrap yard.  Automotive connector are usually pretty heavy duty and some of them are waterproof.  The only cons is that they are not really designed to be removed very often.  Otherwise, you may look on the internet for waterproof connectors that is within your budget (those little beast may cost some big bucks in small quantities).

Edit:
For your package to be waterproof, you can buy an electronics project case made of plastic (choose one large enough for your battery).  You make a hole using a press drill or whatever tool you have that fits the job so that you can put a barrel jack connector.  You may find better prices at other places, but I am not going to do shopping for you.  Also, make sure that your barrel jack's diameter is the correct one.

So, you solder the barrel jack (or its wires) to your battery using a (>20W) soldering iron; you fit your barrel jack connector/wire in the hole you made in the case.  Once everything is correctly packaged, you close the case and you put a small patch of silicon (the stuff they use to seal bath, sinks and so on) on the hole where the wires hang, so that no water may enter in your package.  If the screws/joints of the case are not fit enough, you may also seal them.

Then, you try it and if it works you're done.  Your previous battery's charger should be able to charge your new battery too.