You are not paying CGT on the double.
If you bought your shares for €50k and they are now worth €150k, you are paying CGT on the gain of €100k.
If you buy a property for €150k and it rises to €200k, you will pay CGT on the €50k.
If you leave your money in shares and they rise to €200k, you will pay CGT on €150k. (€200k - €50k)
You should not take out a mortgage to buy an investment property while you have shares. Otherwise, you are, in effect, borrowing to invest in shares. This is not a good idea.
It might be better just keeping the shares and not bothering with the investment property if you want to avoid the CGT hit now.
Brendan