for the record, most freq as a ダジャレ (that woukdn't make a great entry) where 殺し屋 is used literally:
ロシアの殺し屋	738	  
ロシアの殺し屋恐ろし	107	  
ロシアの殺し屋恐ろしや	80	  
ロシアの殺し屋おそろし	69	  
ロシアの殺し屋おそろしや	59

OK. I'm always partial to including things I've actually heard used in real life and I tend to weigh such instances much heavier than the online presence of a word, but otoh this is the kind of word you would expect to explode  in usage online right now even if it had somehow been more common offline than online.

You only get 337 hits for 病院 if you click to the last page of results. This is the number of results that Google has retrieved (and it's always a small number). It's true that Google hits aren't a very reliable metric but a low hit count of the first page is usually a good indication that the queried term is uncommon.
Japanese is absolutely full of puns. I don't think they belong in jmdict unless they're especially common or in a major ref. I don't think this one is anywhere near common enough.

I think it's worth adding, but including "ephemeral" in the comments so it can be checked in the future.

there are only 337 googits for the word 病院
do not take it as gospel