Series-wound motor with DC switching power supply
According to the datenblatt, the PSU is programmable to either deliver constant current, or to deliver constant current and then shutdown after 5 seconds. So it looks like you need not have a problem with shutdown if the winch doesn't accelerate fast enough.

The inrush current from an unlimited supply may well be very high, but as your PSU has a current limited output, that will define your starting current. This means the winch will have a lower starting torque than would be expected for starting from a battery.

As the specified load takes 40A, then at a limited 100A, you will have up to 6.25 times the rated load torque for starting, or less if either of your armature or stator saturates at 100A.