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My whirlpool dryer is making an Intermittent humming noise at or near the motor.
You did not say what if any the problem is or does the unit run OK just hums?

if it was the motor it should it not be a continuous humming?
Usually the humming you see in the forums is from the motor and it will not start.
Some times gas regulators can hum.

Is there any way to diagnose the motor and switch?
If it does not start it is usually shot but cannot tell this from your post.

Should I replace the motor or the motor switch?
Looking at the parts the switch is almost the same price as the motor and switch so if you need it I would go with the motor assembly (Item 62).
Would only replace it if it is not running

my wife is concerned that it could catch on fire.
Have to say this, it is already on fire after all it is a gas dryer.
Sorry, just my weird sense of humor

I opened the access door and the huming sounded like it is coming from the motor area, then the noise would stop for a few minutes then return, but the dryer continued to work.
Without being there I cannot say what the cause is. May even be that something is in the blower wheel. I would try to narrow it down but you will need a good ear. Perhaps try removing it from the exhaust and listening.
Do not run it like this for very long as carbon monoxide is always a concern.

If you do not feel that it is not a fire hazard, I will wait till the dryer stops running before replacing anything
I doubt it is a fire hazard. The motor is thermally protected, also the dryer itself will have a thermal fuse.