Q:

If I use a 19V 4.7A supply to a MAX 250W ATX power supply am I an idiot or should it be safe enough?

I can do the maths, I get near 90W, but I'm only planning to draw under a quarter of the power supplies (ebay link) rated max of 5V/12V combo (estimated load 30W). I therefore consider my 19V old laptop supply adequate plus a little overhead. Reading the listing I see a power rating of 150-250W, I expect that translates to 150W continuous and 250W peak, but who knows right now. I did debate splicing two old laptop chargers together, but worry although it would work I probably should have some protection circuitry to stop them fighting each other.
Am I an idiot? (I accept that I am idiotically frugal to attempt to use old laptop chargers instead of a dedicated high load supply but the cost to recycling ratio doesn't add up)
I understand to a level of intermediate electronics but always considered that an underpowered supply was only a problem if it was truly unmatched. i.e. you were expecting the device to draw the full load or have a relatively high startup(or intermittent) draw then your supply should match otherwise load dependent. Reading Voltage at what Amperage made me question my sanity and proneness to unnecessary fire risk.
Don't get me wrong, I've always advised to have a suitably matched rating on supply and device or ideally over-rated supply to avoid running hot. 
End use devices are various voltage hobby microcontrollers and SATA drives via https://www.amazon.co.uk/gp/aw/d/B07R8S8VTT

A:

If I understand this correctly, you intend to use this "PeakPSU", apparently a cheap PicoPSU knockoff:

...which is a board with a bunch of DC-DC converters intended to generate the usual voltages to power a PC motherboard from a 19V laptop power supply.
The "specification":

Note it doesn't spec all the stuff you'd really like to know about a switching converter or power supply, like how much current each output can provide, output voltage accuracy and ripple, efficiency, acceptable ambient temperature, etc. So you can't know if it will make your motherboard happy.
Also it seems full of cheap "general purpose" capacitors of unspecified origin. Maybe they're the low-ESR models, but there is no way to know. If they are not rated for the ripple current they will take in use, then they will die.
Maybe if you power a motherboard that only requires 30W they will die a bit slower... but they look disturbingly similar to the caps on these ubiquitous fake "LM2596" modules that are everywhere these days, and these are trash. They could at least have invested in a bit of purple paint to make them fake OSCON's.
Why not buy the genuine instead of the knockoff? It will work with your 19V power supply (it says "12-32V input") and it comes with full specifications so you can check the current on each output will be what your motherboard requires, a manual, etc... and it's almost the same price!

