Given this is a Shadowrun setting, there's magic of various kinds. Magic ought to be able to do a pretty good, rapid job of blood degassing. Assuming the society understands the cause of "caisson disease" (not mentioned in 20,000 Leagues because Verne didn't even know it existed, when he wrote in the 1860s), it shouldn't be hard for the magical/medical community to come up with a way to purge the excess nitrogen from the blood and tissues.
Breathing another gas mix won't really help, because other gases (helium, hydrogen, etc.) are also soluble in water/blood to some extent. Heliox is used for saturation diving at great depth, not because it greatly shortens decompression (it does shorten it, but not by even a factor of two), but because it doesn't become toxic in the blood as quickly as nitrogen (40-60 meters is deep enough for nitrogen to start to cause narcosis, so the underwater cities will have to breathe heliox anyway, assuming they know about and can extract helium from natural gas).
Hard hyperbaric suits are impractical because of weight -- 150 m is 15 atmospheres; a soft suit (like a space suit) won't come close to sustaining that level of pressure and allowing the wearer to move their major joints (movement is a problem even at 1 atm relative pressure). A hard suit good for 15-30 atm. will be heavy, however -- including its breathing gas supply, it'll likely weight above 100 kg. Not very practical.
The one kind of reasonably portable pressure support that might work is a skintight suit -- one that literally fits like skin, except over the torso, and provides enough compression to avoid edema and allow circulation to return to the core. The torso would be similar to a portable iron lung, pressurized, and a helmet supplied with the same breathing gas used below, plus pressure bottles and regulator, would complete the ensemble. Not terribly practical, but at least physically possible, in the absence of magical blood degassing.
Another option, possibly more attractive under the desire for steam power, is a hyperbaric perambulator. Basically, a decompression chamber on wheels with a small steam engine. This limits ability to manipulate the environment, but offers the ability to trail a small cloud of coal smoke...