Let’s get reasonable here. Why do you need to operate your garage door from 60m away?

 

The turn down angle of the 4 ground plane radials is ~45. No need for precision there (I've used them flat to ~60° turndown) but the coax does need to be 50Ω which would be RG8, RG58. In a pinch try what you have and see but it's likely the impedance mismatch will induce high Standing Wave Reflection killing the output. The hook at the top is simply an easy way to hang it instead of building a mast mount but is a tuned antenna so make sure it is the correct length before making the bend. And! Hang it with a nonconductive piece of string and not directly on a nail or from a piece of wire.
EDIT: Since this is for a fence gate you are probably going to want to strap a short mast (<10') to a fence post and not hang it from the sky above.

 

Let’s get reasonable here. Why do you need to operate your garage door from 60m away?

See #15

 

See #15

Thanks. I suspected that it was something unusual.

 

OOps, seems I missed the part about it being a remotely located Gate-Opener.

In that case I would have made a different plan ...........
Most likely, the Receiver-Antenna is just a short piece of wire soldered to the Circuit-Board.
Just get a 10-foot, (3-Meters), stick of 1" ( 25mm ), PVC-Pipe and bury 1-Meter of it in the Ground.
Drill a small hole in the side of the Pipe so You can run a Wire inside.
There's your new Antenna.
Don't worry about Coax, or Ground Radials, just a 10-foot chunk of Wire to
extend the "Antenna" and get it higher up in the Air.
.
.
.

 

To put things into context where I live is the Australian equivalent of (for Americans) of Matthew Island.
The nearest fully serviced city is 2848 km away.
Getting what I want is both a challenge and a very long wait.
But the local shop has
50 Ohm RG174U Coax Cable
I have no idea of the origin so I am not sure if it is suitable?

There is a lot more lost in RG174U and in RG58U which should also be available since it is vert common. Check the loss figures for the cables at 433MHz to be sure which is better since good 174U can beat bad 58U.

Because of the nature of the receivers in such devices, the impedance match is going to be very important. They don’t work at all well with a mismatched antenna. The ¼ wave vertical with radials should do just fine if you are careful about the dimensions. The radial length and angle affect the impedance at the feed point, so you should try to stick to the nominal design. A small mast, even just 1m long which a properly built vertical will have a very large impact on range.

A very important thing, currently unknown, is what the current antenna looks like. Can you take a photo of the PCB so we can look at it. Depending on what it is, a close-to-correct impedance antenna could be enough to make a dramatic improvement but just how to connect the new antenna will vary depending on the existing one.