Let me make it a little bit clearer. A TOP267 doesn't output 19V, it doesn't even output a voltage! What it actually outputs is a variable duty cycle PWM via its internal power N-MOSFET output transistor, which connects the pins Drain and Source during its on time. This is normally connected to the low side of the primary of a switching (flyback) transformer, and the other end of the primary is powered by a HV DC bus supplied with either direct full wave rectified mains or via boost PFC, so typically around 170V DC in north America (unless a voltage doubling rectifier is used) and up to about 360V worldwide. The transformer needs precisely pulsed primary current to work. Connecting 19V DC at best wont work, and at worst will burn out the primary and various other primary side components.
The TOP267's Control pin receives feedback from the secondary side of the switching transformer via an optocoupler (six pin IC bridging the L shaped slot in the board a bit to the left of the TOP267EG location you highlighted in orange on your second photo), to precisely regulate the output voltage or put it in standby. The output voltage is determined by the transformer winding ratio and the complex secondary side circuit driving the optocoupler. Your charger appears to have two secondary side voltage rails, one high power, supplied via D201 on the heatsink (top left) ad the other a low current auxiliary supply, almost certainly for the charger control chips, via D202 to the left of the top edge of the switching transformer (big yellow taped transformer in middle of board).
Therefore supplying a single DC voltage, even in the right place on the secondary side, won't make it work. Also Dewalt 18V batteries need more than 19V to charge them. They are 5S LiPO packs so charge to around 20.5V. How much extra voltage the charging circuit needs is anyone's guess. The auxiliary supply is probably much lower, I guess somewhere in the 3.3V to 12V range. Get either wrong, and at best you'll let the magic smoke out, but if you are close, but not quite right there is a risk it may not detect full charge correctly resulting in a damaged battery and possible house fire!