Dell Laptops, and according to the displayed message i would assume AIOs too, talk to the power supply. I am not sure about the details, it is some kind of one wire protocol as far as i know.
It can't talk to your HP supply (i'm surprised it does even fit), so it gives you that warning.
I would also give a similar warning if you connect a too small Dell supply.
And yes, you can skip those warnings (at least you can with the "too small Dell supply") but the system might not start up, might run severely throttled, and/or the battery will not charge.
I suspect that the system will not even try to pull full power, so the supply might be safe, but i am not sure about that. So prepare for your supply to shut down or go boom :p