The Organic Chemistry Researcher in me is Screaming for you to not to apply the DMSO solution to your urethra.
DMSO is one of the strongest solvent used readily in organic chemistry. In general, it is only used after all the hexane & 6-membered ring Halogenated solvents are used. Due to the fact that DMSO is a small charged species of molecule, it assimilates readily around various compounds "cushioning" the various charged parts on the molecule you are looking to dissolve. This "cushioning" is what causes the dissolving phenomenon. DMSO is a very powerful dissolving agent whose inherent charge causes those things dissolved in it to stay "stuck magnetically" to it. The small size of the DMSO molecule and it's charge is also what gives it such a penetration effect.
When first learning of DMSO, my Organic Chemistry Professor made us all stop and put down our pens. She then went on to tell us how much she cared about us individually, and explained that she understood that since a good 40% of the class where student athletes we may be implored to use DMSO to rub into our bodies as it is considered an effective pain treatment and salve. She asked us all to promise never to use it in such a way, simply because you can never be too cautious of having removed everything harmful from the skin. Of course you can kill all germs/bacteria on the skin, but we are talking about things on a chemical level once you introduce DMSO to the situation and in her words, "If it's on your skin, it's gonna travel into your blood stream and into your muscle (etc.) possibly permanently."
As far as a carrier molecule goes, see if it dissolves in Ethanol. All the other solvents I can think of are essentially too toxic to recommend, including Methanol.
My thinking is, if it dissolves in ethanol then you should be able to absorb it without a problem because ethanol absorbs through the skin very easily..... However, you will still have the main issue of avoiding a chemical burn, the same way you would with DMSO.
In closing, bro, please don't put the DMSO into your urethra. Tip toe with its use topically on your penile skin b/c it is very different [much more delicate] than the other areas of skin people have use DMSO on.
Keep a journal and remember that you can tell the stuff working by the presence of an erection, so there is no need to do too much too soon.
In general, things that go into the urethra are benign and none reactive or polarized. Dimethyl-sulfoxide does not fit in that category. If hell bent on urethral use, dissolve in a small amount of DMSO and mix with some thing benign before introducing to urethra.