If ambient temperature is 30°C and you want to keep the LED under 80°C, ignoring thermal resistance from junction to heat sink, you'll need a bit less than 1°C/W heat sink. Passive heat sinks with this thermal resistance exist but they're going to be huge and heavy (about half a kilo, and 200x70x50mm).
Using Mouser search engine, passive heat sinks with dimensions similar to your 40x40x20mm example score about 8-12°C/W so that won't work.
So you have to use a fan, like a CPU cooler.
The example heat sink with fan you link from banggood has no specs but it is way too small anyway.
This one could work but it is too big.
I have no idea how much heat produces an LED like this
About 50W, and the LED should be kept reasonably not too hot (like 85°C maximum).
What is the risk of using such heatsink with a 50 Watt LED? Could the LED blow up? Burn?
With the heat sinks given as examples it'll fry in less than a minute.
Is it possible the sheath of the wires on the back melt?
The LED will probably fry first.
You have to do the thermal design first because that will set quite a lot of constraints on your whole design, like the shape of the enclosure, air flow, etc.
If you don't do the thermal design first then you end up painting yourself in a corner.
Your options are either to pick a cheap cooling solution and then design around that, or use something a lot more expensive that will fit in your current design, probably something like a 1U server cpu cooler with heat pipes and a flat turbine fan that will be very loud.
If you need flat, but can tolerate length, then a GPU cooler from an obsolete GPU could work too.
You could put the fan somewhere else and duct the air through the fins of a passive cooler similar to the one you posted, but you'll have to check its thermal resistance versus airspeed.
It's always a good idea to add a temperature control, or at least a failsafe which turns the LED off if it is too hot, in case dust or cat hair clogs the vents.
Remember the air has to flow, so the enclosure needs enough holes to let the cool air in and the hot air out... and it needs to prevent the hot exhaust air from being sucked back into the fan and recycled... I'm not sure how you intend to build this but if the LED has its back against a wall, then you're going to have to blow the air from one side of the heat sink for example.
