Hello, I'm Keith and happy to help you with your question.
If you retain the property in your sole name there is no disposal and no CGT arises.
Were you to add your son to the title there would be a disposal, albeit of 50% of the value, and there would be CGT on the gain and, as you never lived in the property, the sole relief available would be 11K Annual Exempt Amount and the tax rate would be 18% or 28% or a combination of the two rates depending on your income including the gain in the year of sale. Furthermore it would be a gift and create a Potentially Exempt Transfer (PET) in your Inheritance Tax (IHT) position. PETs run off over a 7 year period at a taper and in the event of your decease within that time frame would be added back to your estate for IHT purposes. If your estate were insufficient to meet the PET then the liability would cascade down to the beneficiary for immediate payment. IHT kicks in at 325K and is levied at 40% flat rate on the surplus.
So after that rather verbose statement we come to the nub of your question. You could not add your son to the title of the BTL property without generating a CGT liability. You can do what you like about the mortgage, that is outside the scope of UK taxation in the scenario set out in your query.
I do hope I have been able to shed some light on your position. I have tried not to rain on your parade.