Actually, the relay needs to be massively over-rated, as it may be called on to make or break the full short-circuit current.
Not necessarily... with the resistance after the reservoir capacitor but before the momentary switch/relay coil/contacts, voltage will collapse if the momentary switch is closed into a shorted load and the relay won't energize. The momentary switch needs to be beefier than expected but, again, the (approximate) short circuit current can be set with the resistor.
If you need a higher trip current you are into DC rated contactor territory, as relays don't have the arc quenching features or contact separation required.
You only need "magnetic blowouts" (aka "arc quenching features") if the load is both high current and inductive in nature, otherwise, you can always put an RC snubber across the relay contacts.
Adding enough resistance to the circuit to limit the short-circuit current may be difficult - it degrades the PSU regulation and, supposing you decide to limit the worst case 'bolted short' current to 60A, for a 12V PSU, that's 0.2 Ohms with a peak pulse power of 720W. Even a 7W wirewound resistor will be marginal, so you'd probably need to go up to 10W.
Yes, I already addressed this when I said that a 5W wirewound resistor letting through a peak current of 10A-20A should be sufficient to protect a 5A relay as long as the caveat that the short circuit current be at least 10x the max load current is followed. That implies a max load current of 1-2A, and so with a 12V supply a resistor in the range of 0.5-1 Ohm should work well.
Really, this isn't rocket science and nobody is (likely) going to lose an eye if things go pear shaped as long as the OP does not try to use this in between, say, the AC mains or a car starting battery, and/or to supply a >10A load. For a 1-2A load at 12V or so it should be fine, and work at least as good as a fuse.
And yes, there are numerous better approaches to limiting current to a load, but in the Beginners section I like to try to encourage the OP to attempt whatever idea they've come up with as long as it isn't too dangerous or flat-out impossible.