You are likely OK.
Cards such as the GTX1050ti mini do not need an aux 6 pin power supply and will run on pcie slot power.
That is a maximum of 75w, leaving plenty in most cases for the cpu and peripherals.
I would go ahead and buy.
If it is a very old unit where the wattage is not mainly for +12v, then reconsider.
The label on the psu should give you the watts or amps that can be delivered to +12v.