About the only STD that you should really worry about is Herpes.  Others are either curable or nearly impossible to transmit via DATY.  According to CDC, there has been no documented case in the world of anyone contracting HIV from DATY.
Herpes, on the other hand, is very easily transmitted. Most people who have herpes don't know they have the virus because there are no visible signs of outbreaks.  Herpes is actually very common among people 12 years old and older.  About 50-80% of the adult population in U.S. have HSV-1 and at least 20-25% have HSV-2.  Those are scientific estimates according to CDC, not my guess.  I also talked to an internist about this issue and he told me that 50% of the people in my age group (25-35) have herpes.  

Most diseases you could contract from it are minor and easy to spot, and easy to treat.  You're not going to get AIDS or a life threatening or debilitating disease from it.

The exception would be herpes.  Ugly and painful, and adds to the risks of other diseases, and might have rough complications.

Your mouth handles a lot of worse things.  Have you ever considered  never eating food due to food-borne illnesses?  Most of those are much worse, and the standards to control them are far too weak.

If you're reluctant to perform DATY, that's understandable.  I am collecting toys for my days when I might not beable or want to offer it.

/Zin