Just5554, please excuse my delay in responding. I want to give a solution to your problem that will work reliably.
Here is the problem as I see it: the 42 V power supply has 1470 uF of output capacitance. The DPS5005 has 660 uF of input capacitance. To charge these capacitors to 42 V, about 0.6 Joules is required (equation: Energy = 1/2*C*V^2). Unless a lossless device such as a series inductor is used to drop the voltage difference between the two units, the resistance of the wires, switch and capacitors will have to dissipate the same amount of energy that is used to charge the capacitors.
The initial current is remarkably high; assuming 42 V with a series resistance of 0.5 ohms, one would see 84 Amps. If a 1 ohm series resistor is added to limit current, the initial current will be 28 A. This will cause a problem though, at maximum output current of the DPS5005 of 4 A, the 1 ohm series resistor will have to dissipate 16 W.
The switch will take a finite time to close. As the switch is closing and the contacts are just beginning to touch, the current is concentrated in a few very small areas. If the contacts are not capable of handling the current, the material will first melt then solidify thus welding the contacts together.
here is a link to a problem with relay contacts sticking:
https://www.eevblog.com/forum/projects/relay-latching-and-getting-stuck/An NTC thermistor could be used but it would have to have a high enough cold resistance to limit current to something the switch could handle, yet it would need a low enough resistance to not drop too much voltage at full current. Also, there could be a problem when going from zero to full output load current. The thermal time constant may be too long, and it will limit current until it comes up to temperature.
I could not find more information on the Epson power supply. What is the maximum output current? Does it have any control wires in addition to the output wires?
I went to the website for the switch but I cannot see a current rating of any kind. Does the switch have any ratings printed on it?
What is your experience with electronics? Would you be able to construct a small circuit with one or two transistors, diodes and resistors?
I've worked out a circuit using a 2N6284 darlington transistor rated for 20 A, but haven't completed the analysis.