You can always go to ftdna.com and order the 111 Y test -- you can also talk to the project coordinator for your haplotype and for $800 or so do a walk-the-Y to sequence many kbp of your Y. The base test is much cheaper and would at least indicate if you're in the same ballpark.
You aren't transmitting your genome over the Internet or anything like that because the bits of DNA that you are thinking about are never sequenced. Your DNA gets sent to a university medical facility and only the Y/mtDNA are sequenced there. Those bits of sequenced information are basically useless for any of the scary situations you're imagining. The medical lab turning over your actual DNA would be akin to your doctor turning over your DNA to a government agency. Are you going to stop seeing doctors too?