Rashi explains (14:34) that Moshe knew that the "mekoshesh eitzim" was mehuyav mittah, but he didn't know which one because it wasn't said anywhere befeirush. Why didn't Moshe apply the rule that stam mittah in the Torah, if not specified otherwise, is henek?
Source for rule: Sanhedrin 52b
(ויקרא כ, ב) מות יומת בחנק אתה אומר בחנק או אינו אלא באחת מכל מיתות האמורות בתורה אמרת כל מקום שנאמר מיתה בתורה סתם אין אתה רשאי למושכה להחמיר עליה אלא להקל עליה דברי רבי יאשיה “Shall be put to death” means death by strangulation. Do you say that his execution is by strangulation, or is it rather by one of all the other types of death penalty stated in the Torah? You must say that it is by strangulation, as everywhere that the death penalty is stated in the Torah without specification you may not take it to be more stringent with regard to it, i.e., to mean that the sinner should be sentenced to a severe type of execution; rather, you must take it to be more lenient with regard to it, i.e., that a lenient type of execution should be applied. Consequently, the sinner is sentenced to be executed by strangulation, which is the least severe type of capital punishment. This is the statement of Rabbi Yoshiya.”