Ungrounding an Amp--Any Danger?

Your preamp should be the only grounded component to achieve the lowest noise floor. The other components drain to ground through the interconnects, to the preamp, and then through the preamp's grounded power cord.

Danger will then be present if you either

A.) Unplug the preamp from the wall, or
B.) Remove the interconnects between a (ungrounded) component and the (grounded) preamp, or
c.) Both

If you use a cheater plug(s) on a component(s) to eliminate hum (ground loops) just make sure the component has a path to ground -- usually through the ICs and the preamp. If you need to rearrange your stuff, just turn it all off AND unplug it first (which you should do anyway!)

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Try using a 3 prong adapter with the ground pin out first.

The idea in "star-grounding" is to leave the component with the highest voltage potential -- the amp -- grounded, and to unground everything (everything) connected to it.
BUT, if you want to determine if the hum is intrinsic to the amp, just disconnect all inputs, so that the integrated has ONLY the speakers still connected. If there's hum through the speakers when you turn the unit on, then you'll know that the problem is not due to a ground loop. If there's no hum, then you may want to try star-grounding.

Ground protects you from being shocked in the event of an internal failure. Cheater plugs are routinely used to locate/cure ground loop issues. Violates electrical safety codes, hence the warning.

Defeating a three prong power cable with a "ground lifter" etc., is not only dangerous, it defeats the UL listing (Underwriter Labs is an independant body which tests electrical devices for safety under extreme conditions), and will invalidate ANY and ALL insurance claims that occur as a result of that equipment. The ground is there for a reason (aside from causing ground loops): in the event of electrical fault within the equipment (caused by internal or external forces), the ground acts as a safety to safely shunt excess current away from the chassis and you. Solve your hum problem by finding out what is causing the hum in the first place.