I was informed today that one does not say the above today as hallel was said.
Does it make a difference whether Hallel was said with a Bracha or not?
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Kehillat Shaarei Yonah Menachem, an Ashkenazic synagogue in Modiin, Israel, said הלל with a ברכה before and after, and also קל מלא, but skipped תחנון, on יום העצמאות 5779/2019. I know because I was present at the time.
Common Nusach Ashkenaz minhag that I have seen is that El Maleh is not recited when Tachanun is not recited. (I believe that you will find such instructions in Art Scroll and Birnbaum Siddurim among others. It is also a common instruction in the Luach Ezrat Torah pocket guide on days when Tachanun is ommitted.)
Yom Ha'atzma'ut, of course, is not mentioned in Shulchan Aruch, so there are various customs regarding the recitationl of Hallel vs. Tachanun. However, you will find a common theme that when Hallel is said, Tachanun is not. Thus, for those minhagim following the overall custom, El Maleh would also be omitted.