Your problem lies in the way TENS units operate.
This site shows how a simple one is built.
This is the circuit diagram from that site:
The output uses a capacitor in parallel with the transformer to form a resonant circuit - this makes the output voltage higher than if there were no capacitor.
When you are connected to the TENS device, your body acts as a capacitor (and as a resistor.) This damps the resonance.
Because of this, the output voltage is lower when you are connected than when you aren't. Or, put the other way around, the output voltage is higher when you aren't connected.
TENS devices usually operate in pulses. But, you can't guarantee that your relay will switch between pulses. So, sometimes you might get a smoother switchover (no jolt or weak jolt because you switched between pulses) than other times (major jolt because you switched in the middle of a pulse.)
Because of the resonance, there's probably not a time when there's no signal present at the output.
What you would have to do is to switch from "connected to you" to "connected to an electrical dummy of your body."
You would use a relay to switch between the two instead of simply open or closed. You might need something faster than a mechanical relay, since the TENS device can create pulses faster than a mechanical relay can switch.
An "electrical" dummy in this case would be a resistor. A few kiloohms ought to do. If the resistor value is too high, you will get jolts. If it is too low, you will get a sort of "fade in" effect where it takes a pulse or two to get back up to the desired intensity.
You seem to be using a real, medical TENS device. Hence your reluctance to modify it. I'd go a step further and say you shouldn't modify the treatment plan, either. Use it as prescribed, and don't experiment.
If this isn't a medical device, I'd still say "leave it alone." You can hurt yourself with those things if you mess up. The level of your question says you don't have the skill or knowledge to play with high voltage devices connected to your body.