Short answer: Yes, but ... and the "but" might be a little too much for you to deal with.
Now, let's deal with the electrical stimulation of a nerve scenario that is described in your question. This is also a sort of a "yes, but" issue. It is most certainly possible to stimulate a nerve and see a response on a skin electrode over where that nerve travels. It's done all the time, especially in clinical nerve conduction studies to make sure there's no problem with the nerve. That said, this isn't often a "stimulate once, record the response" type of study, for a number of reasons. The signal is very small, and it's riding smack dab in the middle of much larger noise and EMG signals. Also, the artifact from the stimulus pulse can be much larger than the signal of interest. With respect to the stimulus artifact, the artifact will get to the recording electrode faster than the action potential will, based upon nerve conduction velocity.
The way this is done correctly is called ensemble averaging. You use the stimulus pulse to line up N responses in time, and take the average of all the responses. The artifact and the response will be correlated in time with the stimulus, and get reinforced by the ensemble averaging process, and all the other signals won't be, and will get averaged out. So, you'll see a stimulus artifact, followed by a delayed response. The math says that the uncorrelated signals get attenuated by a factor of \$\sqrt{N}\$, making this a very powerful tool.
Now, the artifact is so big and robust compared to the signal and noise, that it's very easy to convince yourself that you're actually looking at the response you expect, only to be observing the artifact! So, unless you're ensemble averaging, and see the delay you would predict from nerve conduction velocities, chances are very high that you're fooling yourself.
It certainly is possible that you can record the response properly, so now let's start to develop the answer to your question about vibratory stimuli.
Once again, the response will be very small when recorded with a surface electrode, so you must move to ensemble averaging techniques. A vibratory motor might do it, but there are a variety of different kinds of "touch" sensory organs, and the frequency response of some of them might be too slow to produce a time-locked response, and might just respond with a general increase (or decrease) in action potential frequency. With the skin electrode, you will need a time-locked response to see it with ensemble averaging techniques. Then, you'll need the signal to time-lock too-- maybe a pulse-per-revolution signal from the vibratory motor would do it, if you can figure out how to get that.
One other trick comes to mind, that circumvents frequency response of the sensory apparatus, and is very easy to use for ensemble averaging. The lab I worked at as an undergrad many years ago used it. We were using microelectrodes to record signals in rat spinal cord, in response to electrical stimulation of the renal nerve. When we found a response to that, we would try to determine if the fiber received any projections from sensory fields on the skin. To generate a nifty time-locked sensory stimulus, we glued a pin to a speaker cone, with the blunt head facing out, and we sent a pulse to the speaker, causing the pin to poke the animal. We could do this hundreds of times in short order, making it easy to ensemble average. Granted, because we were using 4 \$M\Omega\$ microelectrodes, and the electrode tips were a few hundred microns at most from the spinal cord fiber, our signals were huge compared to what you're talking about, but the technique would be the same.
As to the second part of your question, you'd need to get up close and personal with google scholar. I took a quick try at it, and most studies go the other way, i.e., the effects of sympathetic stimulation on tactile sensory apparatus (e.g., https://www.sciencedirect.com/science/article/abs/pii/0022399963900011) -- and you're looking in the opposite direction.