You can buy properties in Turkey remotely also . You can contact any Broker/agency/lawyer directly to book your online viewing trip. Ask them If they accept cash.
Or open a multiple bank account and deposit in cash and Them merge them into one.
Than Pay for Property.
There is no issues with that. Usually when you buy you go to the notary with the cash, transfer the real estate and pay the to the person amount. It is not the securest way but it is definitely possible. In addition you can also hire somebody to come with you and handle the process. Better alternative would be bank transfer.
Be sure to hire a local, external estate agents (who doesnt sell you the real estate) which will help you in the whole process. There is a lot of scam going on with foreign buyers.