First of all, you need to observe the nature of a cordless drill’s battery pack. It can deliver a higher amount of currents, substantially more significant than the charging current.
When voltage comes from an external source, matching the output voltage of the battery pack is only the beginning. It must also deliver that extremely high current, which necessitates that the drill’s wiring is rated for that current as well.
18V to 20V Adapter
EnerTwist Rotary Tool Kit
USB Light Bulb Adapter
When it comes to cables at that current, the battery pack is probably 20v or less, so there’s not much voltage to spare. It’s pretty improbable that you’ll be able to fit a mains power source with the needed voltage and current inside the existing battery pack’s volume or weight. To “balance” the drill and make it pleasant to use, you will need to offer something of that weight and placement. The weight distribution has developed with the battery pack in mind.
You’re presumably thinking of adding two heavy-duty high-current insulated additional flexible wires to an existing battery pack (for ease of connection, balance, etc.) and running them to a power pack in a Figure 8 pattern. The latter can come in the form of a belt or a backpack. You could just put a large battery pack in there to get some of the benefits of both corded and cordless. It would still require charging, just not as frequently.
If not, you’ll need a mains power source with a 20v 20A output, depending on which cordless drill you have. It may require additional power, such as 20 volts and 40 amps.