Both ammonia and methylamine are totally stable as aqueous solutions which you could definitely get an NMR of those solutions. You can also buy solutions on methyl amine in THF, MeOH, and EtOH and ammonia solutions in MeOH, EtOH, iPrOH, or dioxane, all of which are fine NMR solvents. Shouldn't be a problem. The smell thing should be obvious because it's pretty tough to deal with significant amounts of either of these chemicals without smelling them.
It's also possible to do gas phase NMR, incidentally.
The chemical derivitization is definitely a good way as well, it's just less direct and would take more time.