As per the above, either waiting for (fairly) certain cool weather or getting a salvage fridge are the main options.
A central heating room thermostat (or rather one that can control aircon *cooling* - usually described as having "changeover" contacts) controlling the power to the fridge (ideally just the motor) should give you control over temperatures above the range of the fridge's own thermostat. Unfortunately, it also means switching 240v mains inside the fridge. Which isn't something that can be recommended as being wholly safe under all circumstances.
However there are thermostats which have a radio link between the measuring/setting unit and the mains switching relay... giving mains isolation, but what I don't know is whether the fridge casing screens the radio signals.
You can't control the humidity in a garage very easily. There are things you can do to control the humidity in a fridge.
As Tristar says *salt* can be used to control humidity to a set point of 75%, which is useful, if a little high. 60-70% is usually considered ideal for air-curing.
The way salt works is that a saturated solution would control to 75%, anything *less* than saturated would control to a *higher* humidity.
A simple solution doesn't *de*humidify very well. The extra water taken up dilutes the surface layer, which becomes less than saturated and so controls to a higher humidity.
The way round this is to have a pile of wet salt rather than a dish of solution.
The more surface area you can get, the more powerful the control action.
Note that the cold chiller elements will tend to be the site of condensation, dehumidifying the enclosure when the fridge is cooled.
A tiny amount of air movement (but not a blast) is a good thing - both to even out conditions and to discourage mould, so a tiny ex-computer fan mated to a bit of plastic pipe can come in useful.
Using a fridge also saves most of the concern you might have in the garage about dust and insects.
A "larder" fridge *without* an icemaking compartment is preferable, giving you more usable room - but I've read of people doing wonderful stuff in a small "drink chiller" cabinet.
If you can set it up in your chilly garage, the fridge will use hardly any electricity to maintain an internal temp below 15C.
"Air curing" a whole ham, on the bone, is not considered an ideal project to start with. Just as one consideration, it takes ages! And success isn't guaranteed. Personally, I kinda suspect that there are butchery considerations particular to whole leg curing... Since you've picked up on the 15�C, I wonder if there's anything on butcher pre-cure prep that you've encountered?
You could probably start more simply with salami and small cuts of meat. That should also help to give you confidence that you have food poisoning under control!
And if you want to make "ham", you could have a bash at some brine cured, "boiled" ham (its simmered really) and maybe even bake a glaze onto it.
You can make a nice ham in a traditional British style from a piece of leg of pork that the butcher has prepared for roasting... and a bowl in the family fridge is about all the hardware you need
Do keep us updated on your progress!