If the venom is anything like most other venom in the animal kingdom, the venom proteins would degrade fairly quickly. I kept rattlesnakes and some other vipers for many years and did allot of venom research. The proteins are not very stable and in a matter of days it looses its "bite" so to speak. Moisture and heat degrade it pretty fast. That is why in the "anti-venom" industry the venom that is stored for any length of time is freeze dried.
I would think that ray venom has proteins or compounds that help the venom hold up (not dissolve, disperse or break down as readily) in water better than say, rattlesnake venom or spider venom due to the fact that rays evolved in water and so did its venom. So a shed stinger in an aquarium will probably "hold" the venom until it degrades but that would be just a guess because I have no lab experience with ray venom.
But like it has been said, the ray stinger is not a hypodermic type delivery system like a rattlesnake fang. It does not inject the venom but instead works like the arrows of the South American tribes that rub there arrows on Poison Dart Frog backs. The venom is on the stinger and if the stinger goes in your flesh then so does the venom.
I can see how handling a barb could give you a tingling sensation as the venom could "absorb" through the skin if there was still "active" venom on the barb. I have been struck at by rattlesnakes and had venom sprayed/splattered on me and if I left it on my skin to long, it would start to tingle and ache. If it were to get into a cut or scratch, it could cause a mild envenomation. When this happened I would have to change my cloths (and wash them) so it would not be sitting on my skin all day.