Sure, if you want to desolder the power connector on the motherboard, you can replace it with a barrell connector. Then do the same for your power supply. I don't have enough confidence in my electrical knowledge to know that this will work, but I'd assume it would.

its Dell so most likely one of the pins is ID so it would have to be Dell 3 pin barrel jack (power at two sides of the barrel, id on a pin)
mobo connector https://www.ebay.com/itm/110939955823
pcb

There is one universal charger with a converter Laptop Charger BB-165892
magic ID pin is a 1 Wire EEPROM and probably hiding in that converter to lie to the laptop about being genuine charger 😀
Definitive way to solve this is what ldeveraux described, either replacing with Dell specific barrel jack (3 pin) or standard barrel jack and transplating 1 Wire EEPROM from spare DELL charger.

edit: forgot I have a diagram 😀

3rd pin is optional AIR_ADP#, apparently digital "airplane adapter" going to ground in case charger is supplying limited power, connects to MB3878 and limits charging current = slower charging with weaker PSU connected.

TLDR: can ignore third pin, replace connector with ordinary Barrel jack

AFAIK, there were two types of PSUs: the PA-6 (20V, 3.5A) and the PA-9 (20V, 4.5A). If a weaker power supply was used with a laptop that required higher power consumption, the CPU would run only at a reduced clock speed—for example, a P4M 1.8 GHz@PA-9 was reduced to 1.2 GHz@PA-6. I don’t know if the PSU type detection was related in any way to the design and wiring of the connector.