It is true that the expressions have unique set phrase definitions, so each would be preferable for its specific use:
Something known by most people:
it’s common knowledge that no one has yet found a cure for cancer
ODO
noun
[MASS NOUN] Knowledge of a broad range of facts about various
subjects:
this quiz tests your general knowledge
[AS MODIFIER]:
a round of general knowledge questions
ODO
But it would be quite parochial to impose the set phrase interpretation. The adjectival elements of each expression are similar in their meaning and both can be combined with the noun knowledge with insignificant shift in meaning:
Common
adjective (commoner, commonest)
1.0 Occurring, found, or done often; prevalent:
salt and pepper are the two most common seasonings
common misspellings
it’s common for a woman to be depressed after giving birth
1.3 Ordinary; of ordinary qualities; without special rank or position:
the dwellings of common people
a common soldier
1.4 (Of a quality) of a sort or level to be generally expected:
common decency
1.5 Of the most familiar type:
the common or vernacular name
2.0 Shared by, coming from, or done by two or more
people, groups, or things:
the two republics' common border problems
common to both communities
2.1 Belonging to or involving the whole of a community or the public at large:
common land
ODO Emphasis added
Common knowledge yields the reasonable meaning:
Ordinary knowledge belonging to the whole community
vs.
General knowledge yields the reasonable meaning:
Normal knowledge affecting all people
General
adjective
1.0 Affecting or concerning all or most people or things; widespread:
books of general interest
the general opinion was that prices would fall
1.1 Not specialized or limited in range of subject, application, activity, etc.
brush up on your general knowledge
1.2 (Of a rule, principle, etc.) true for all or most cases.
1.3 Normal or usual:
it is not general practice to confirm or deny such reports
ODO Emphasis added
Alternative:
adjective
1 [ATTRIBUTIVE] (Of one or more things) available as another
possibility or choice:
the various alternative methods for resolving
disputes
ODO
Common knowledge is about half again more common than general knowledge in the corpus, but they have been roughly tracking together for about 75 years:

Conclusion
It is certainly appropriate to interpret common knowledge and general knowledge as set phrases, but neither phrase is dominant enough to exclude the simple combination of the words. Therefor, in appropriate contexts general knowledge remains an acceptable alternative for common knowledge.