N/A

It is a very accepted practice to use the original Japanese names for the different genres of Japanese art (ukiyo-e, shin hanga, etc.). I personally use original names, too, in these circumstances.

Like with wasabi, obi, tsunami, etc. original Japanese names are used with an explanation if needed.

"Asobi-ye" is layman's term for "Giga 戯画" about which the most well known is 鳥獣戯画. See below:

http://ja.wikipedia.org/wiki/鳥獣人物戯画

It is a "cartoon" in today's term, but sometimes falls in the category of arts called "calicature" as it can be a political satire.
They can be an educating tools for kids and adults alike, as well as entertainments.

I understand Joyce's point, but I believe these two terms are right on the target that help readers' better comprehension (thus eliminating the strain of eyes to read explanatory sentences).

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Note added at 10 hrs (2009-11-01 17:37:28 GMT)
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Woops, I forgot to say "Edo Era", so whole answer is "cartoons (or calicatures) of Edo Era".