How do we know what is or is not necessary to do the Joining? I could have sworn that there was a conversation or a codex or something that mentions that the joining juice has to be specially prepared. If that's not the case then why didn't the Warden and Alistair just start a warden recruitment drive in order to up their chances of being able to kill the archdemon?
The wiki article states that the Joining requires an extremely potent dose of the corruption and that the potency of the blood used can be magically enhanced, but it doesn't say that that's the only reason that lyrium is used. Further, the article also refers to the process as a blood magic, which would seem to imply that it's more than drinking particularly tangy blood.
Nevertheless, the only fluid that I remember people saying is particularly virulent is blood. There is no reason to assume that the taint can be spread via sexual fluids just because it can be spread by blood*. Similarly, there's no reason to believe that it can be spread by sexual fluid just because the taint can make someone infertile.
*As far as I know, it hasn't been suggested that coming into contact with Grey Warden blood is dangerous for anyone at all.