(I ran out of time to look up and provide sources beyond those for the central point. This answer is known to be incomplete. I am posting it now anyway with plans for further editing so that (1) I don't risk losing what I typed so far, and (2) I can crowdsource the job of finding those sources. So rather than downvote before those edits, how about contributing to the effort?)
As a prelude, we should clarify that there are actually two uses of the expression "halakhah leMoshe miSinai":
First, it is used literally. A law given to Moshe from Sinai. Sinai here is broad, meaning the wilderness, not the mountain. There is no guarantee that this particular detail was received during Moshe's 120 days atop the mountain.
Second, it is also used idiomatically, "as sure as if it were given to Moshe from Sinai". This idiom is used for laws that were known to be rabbinic enactments. It even later got used in Ashkenaz to refer to Nusach haTefillah -- traditional tunes used by chazanim.
I will limit this answer to the first, literal, usage.
What does it mean that the law is categorized deOraisa? The most notable pragmatic difference is that we err on the side of stringency when a doubt arises in a Torahitic law (safeiq deOraisa lechumera); while if the law were deemed rabbinic, we are permitted to be lenient in cases of doubt (safeiq derabbanan lequla).
Among other potential pragmatic differences is that one person can only fulfill an obligation on behalf of another if the person doing the action is equally obligated. A person who is only obligated deRabbanan could not fulfill an obligation for someone who is obligated deOraisa. But the issue of safeiq (doubt) makes an easier to find litmus test.
One last clarification before getting to actually answering. There is a middle ground between deOraisa and deRabbanan. Megillah reading for men was legislated by the Anshei Keneses haGedolah (the Great Assembly; the high court of the early 2nd Temple period), and therefore is not deOraisa. However, among the members of the legislating court were many prophets, so that the law had Hashem's imprompeteur. It is not just another rabbinic law. In contrast, it is rabbinic law that women hear megillah. For this reason, the aforementioned rule applies: because a woman is less obligated to hear megillah than a man, a man cannot fulfill his obligation by hearing a woman read. Some sources understand the term "divrei soferim" as referring to this middle ground -- prophet endorsed rabbinic law. After all, sages of this period are often called by the term "soferim", such as "Ezra haSofer".
So, after all that, I would reduce your question to: When a law is deemed halakhah leMoshe miSinai in the sense that Moshe actually was given the law by G-d, would doubts in that law be ruled stringently? If so, it would make sense to apply the term deOraisa. But if not, we would need to see if other bellwethers apply. If the results are mixed, perhaps halakhos leMoshe miSinai also sit in the middle ground.
Measures (shiurim) are halakhos leMoshe miSinai (Yerushalmi Pei'ah 1:1, Bavli Sukkah 5b, Yuma 80a). But when measuring something for the sake of a mitzvah deOraisa, we rule stringently. (Rav Avohu on Niddah 58b, and invoked by Tosafos, Berakhos 26b). We do not consider having the necessary size / weight / duration a rabbinic amendment to the original deOraisa law.
So it would seem that from a pragmatic point of view, the answer to your question would be that they are deOraisa.