FDR's condition was not entirely a secret, having been mentioned at times in newspapers and magazines - especially around the time of his first election and subsequent campaigns (in passing, not as criticism). It does seem that efforts were made by FDR and his team to both downplay the condition and to project the idea that his condition was improving, but after enough years, and with the sort of diplomatic communications that go around, it is likely Churchill was aware of his limitations. There is a Time article about this here, debunking the notion that it was a secret, or that the press had out an all-out blackout on coverage of the topic.

As far as Axis propaganda featuring Roosevelt's disability, it seems to be fairly rare. I can locate only two examples showing it (though I'm sure there are more), and in neither case is it the focus of the piece in question. On this propaganda postcard he is pictured with a cane, which I wouldn't necessarily say was even put there for propagandistic reasons (any more than a cigar for Churchill - it was just something he carried). I'm sure there are others out there with a cane, but that alone isn't exactly insulting. An example that may be cloesr to home is this piece created by the Nazis for use in Serbia, which features Roosevelt on a crutch. While such an image might be invented simply to imply an enemy is weak, it seems that the particular inclusion of it in this case is likely a riff against FDR's known mobility troubles. Again though, it doesn't especially stand out against the backdrop of other propaganda caricatures.

Additionally telling might be these example posters from Italy and Japan, which definitely portray him in a fairly assertive and strong way as representing a dangerous enemy to be fought, rather than simply mocked.