Collins Dictionary clearly states the difference between BrE and AmE usage,
like the cat that got the cream BRITISH
or like the cat that ate the canary AMERICAN:
If someone looks like the cat that got the cream, they look satisfied and happy with themselves because they have been successful or done something they are proud of. `Thanks a million,' he repeats, grinning like the cat that got the cream. Jules stands at one end, looking like the cat that ate the canary.
while M-W doesn’t cite any specific geographical usage.
Google Ngram shows a wider usage in BrE than in AmE of “the cat that got the cream”, so its reasonable to assume that the expression is also known in the U.S. where “the cat that ate the canary”, is, however, more commonly used.
The idiom carries no innuendo, but given that it appears that the “cream” version is not popular in the U.S., whether it may be misunderstood and innuendo inferred very much depends on the person involved.