One thing that can help is if you get lucky with a fingerhack, as it is a bionic. There may be a crafting recipe for one. Other than that, I will say that the card reader itself can be smashed, I don’t remember if its easier or not, but one potential out is to take out the card reader tile and escape that way.
If you have z-levels enabled, one tactic is to break the ceiling and use some furniture to climb out. Related to this, and this is RNG, a giant mole rat can be your friend here since they tend to do a lot of damage. Even if you can’t lure it up a z-level, they usually destroy things down to the rock walls surrounding the labs, which can be used to tunnel upwards.
if all else fails, use fire.