Departure and arrival procedures often prescribe airspeeds which must be maintained at certain fixes. 14 CFR 91.117 sets rules for airspeeds but has a paragraph which states that the airspeeds don't apply if the aircraft can't operate safely within those limits. Does any regulation or published recommendation alleviate aircraft from the airspeeds prescribed on instrument procedures for similar reasons?
The wording of your question seems to suggest that 91.117 doesn't apply to instrument procedures, but there's nothing in the regulation itself to say that. Specifically, 91.117(d) is very broad (emphasis mine):
If the minimum safe airspeed for any particular operation is greater than the maximum speed prescribed in this section, the aircraft may be operated at that minimum speed.
Having said that, if you can't comply with any procedure or instruction you should inform ATC and let them tell you what to do. The AIM mentions airspeed in the context of holding (section 5-3-8), but it's reasonable to assume that you should inform ATC in any scenario where you can't comply:
Pilots unable to comply with the maximum airspeed restriction should notify ATC
From the ATC side, the ATC orders have an entire section (5-7) on speed adjustments, but one of the first things it says is:
It is the pilot’s responsibility and prerogative to refuse speed adjustment that he/she considers excessive or contrary to the aircraft’s operating specifications.
So if you can't comply with an airspeed restriction (or any other restriction) just tell ATC "unable" and work it out with them; that's what they expect, based on the ATC orders.
§ 91.3 Responsibility and authority of the pilot in command.
(a) The pilot in command of an aircraft is directly responsible for, and is the final authority as to, the operation of that aircraft.
(b) In an in-flight emergency requiring immediate action, the pilot in command may deviate from any rule of this part to the extent required to meet that emergency.
(c) Each pilot in command who deviates from a rule under paragraph (b) of this section shall, upon the request of the Administrator, send a written report of that deviation to the Administrator.