Are there sensors that can detect a rip, crack or damage in the fuselage skin by not using air pressure differential on aircraft?
Such sensors certainly exist. The sensor is as simple as can be: usually a piece of wire. The bonding of the wire to the skin or structural elements dictates what kinds of damage it's sensitive to.
The "wire" can be in the form of a thin metallization on a thin non-conductive substrate that's intimately glued to the skin - such gives the most sensitivity to cracks, and is a crack detector.
If you wish to detect whether the rocket is in the process of breaking up, you simply need to run a thin, insulated wire along a longitudinal structural member, such as a tank, and attach it in a few places, but certainly rigidly at the ends. The input is used sometimes for automatic flight termination.
The major problem with pressure differential sensors is that you really need a big hole to overwhelm the pressurization systems on turbine-powered transports. A pencil-sized or even coin-sized hole is noisy but essentially irrelevant, and no, you won't get sucked out through it.
Why is it so? For cabin ventilation to work to begin with, there must be an outflow valve. Such valves, in steady state, have openings way larger than a coin. The more unplanned-for holes you add to the pressurized section, the smaller the outflow valve's opening will be. Only when the outflow valve completely closes and the pressure is still insufficient, you've got a problem...
So yes, the outflow valve's position in steady state can be used as a measure of air leakage elsewhere.