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There are lots of plastic waterproof boxes available, you can drill a hole in them and put a waterproof gland on it. Feed the mains in and put a socket on it, then plug in. Or go commando and solder the mains to the pins or even split the transformer apart and wire the mains directly onto the transformer board.
There are a lot of other options if you are prepared to buy specialised transformers etc.
I got an outdoor camera/floodlight to replace an existing outdoor light.
Intention was to chop the plug off and wire it to the existing supply using an outdoor junction box. Turns out though that it's a transformer plug so that doesn't seem to be an option.
It's also hard to tell if outdoor socket boxes have enough space for them, lots seem to only fit a 13A plug.
Any bright ideas to install it?