battery charger

Not practical to build one. There are so many features already built in to the commercial ones that it may prove potentially disastrous to attempt it.

Overcharge protection, Excessive current, condition lights etc. are features that one just can't duplicate practically on a custom basis.

Why don't you call up the company that makes the equipment and see if they don't sell replacements.

If you call customer service, they may actually ship you an exact replacement after less than an hour on the phone. Or not. It will likely cost about $20 which may be about what you paid for the cordless tool. I say try your home made charger. Ac or dc? It may tell next to the jack. Sometimes the diodes are in the power cube, sometimes they are in the tool. If unsure try dc first: It may charge the battery even if the original power cube supplied ac.
Start by searching your house for power cubes, put ac ones in one box and dc in an other. Try to find a plug that fits in the jack on the tool. They only make about 666 different kinds, but you may need one of the more common types and sizes. (alligator clips will likely be a pain) If you find one and the cube is dc you have good start. If not, you can often find power cubes at yard sales for a dollar or two sometimes including the device the power cube was designed to power.
!8 volt power cubes are quite rare, so the first one you find may be 7 volts. Cut one wire a few inches from the cube and splice in the two wires from a 9,10,11, or 12volt power cube with about the same current rating. If you get the connections wrong, you will measure the difference voltage, about 2 volts instead of about 20 volts. If you don't have a voltmeter use 5 or 6 lights from a defunct string of miniature Christmas lights. They will light about normal brightness at around 20 volts. They will light very dim on as little as one volt each.
A minute or two after you start charging touch each power cube. If one or both are hot, you need to let them cool, before you charge some more to avoid failure of a power cube. Warm is normal, but hot is not. After an hour or two check again, and check the battery you are charging. If it is more than slightly warm, the battery is likely charged. More likely it will take longer to charge than with the original charger. especially if the power cubes are smaller than the stolen charger. Over charging shortens the life of the battery, and often the original charger will over charge, so check the battery temperature even when using the correct charger. Neil