The word ᴱQ. men (mem-) “nose, beak” appeared in the Qenya Lexicon of the 1910s derived from the early root ᴱ√MEME (QL/61).
Neo-Quenya: In later writings, Tolkien used ᴹQ. nengwe for “nose”, but I think it might be worth adapting this word as ᴺQ. mén (mem-) “beak”, with a long vowel to help distinguish it from Q. men “way”. This derivation is similar to ᴹQ. kén (kem-) “soil, earth” < ᴹ√KEM from The Etymologies of the 1930s (Ety/KEM); hat-tip to Röandil for suggesting this comparison and the form mén.
A noun appearing as ᴱQ. puntl in the Qenya Lexicon of the 1910s under the early root ᴱ√PU(HU) “generate”, with an erased gloss “mem. vir.” (QL/75). As suggested by the editors, “mem. vir.” is an abbreviation of Latin “membrum virile” = “male organ”, hence “✱penis”.
Neo-Quenya: I would adapt this word as ᴺQ. puncil “male organ, ✱penis” based on a Neo-Root ᴺ√PUK.