I’d say the most standard way for a negative command is a construction with ava-: avo nago “do not kill!” (That does not carry the same stylistic implications, but we know for certain that it’s grammatical).
Regarding the (a)tha-future, Tolkien devised two paradigms:
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Quendian & Common Eldarin Verbal Structure (late 1940s), similarly in Common Eldarin: Verb Structure (early 1950s):
Future. All the Eldarin languages express a simple future inflexionally, but the inflexions and patterns used are different [...] In Old Noldorin the future was usually expressed by adding -thā to the aorist stem: matithā- “will eat”. This thā is probably in origin a defining adverb = “then, next”, since with time-reference the pronominal stem √THA in Noldorin referred forward (PE22/96-97).
That’s the paradigm you are using, which gives you the i-mutation in dag → deg·i·tha-. Here this construction is a simple future, so there shouldn’t be any problems with negation.
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Late Notes on Verb Structure (1969):
In S. the verb aþa, atha had become agglutinated to the verb stem, and formed a kind of “future”, expressing the intention of the subject, closely resembling in sense and uses English will (when not mere future): “I will (I’ll) go, he will (he’ll) go”, espec. in the 1st and 3rd persons. In the second person the implication of “will” of the subject is clearest in questions or negation. Cf. song in LR, linnathon “I will sing, I intend to sing”. This was a fairly late development, as is shown by the fact that aþa, aþon etc. could still be used with ellipse of the verb stem, as e.g. in linnathol? “will you sing (please)”, answer aþon “I will”. Apart from this athon “yes, I will” (or in plur. athof, athab) the verb atha- was no longer “free” (PE22/167).
With this etymology we get no i for stem verbs caw- → cawathon. Also the meaning has shifted to “intend to do” (there is also a simple future based on TUL-, tolen cared “I will do”), so negating it (“thou doest not intend to kill”) might not be the sense you are after. Also it is dubious if negation + atha- is even possible in this paradigm:
“to be willing, consent, agree”: positive of √ABA “refuse” but naturally less often so emphatic. It was, however, similarly constructed. The element found in Eldarin appears to have been an old one, a “mono-consonantal reversible” ÞĀ̆/AÞA. (PE22/165).
You could read that as “for ú·atha- use ava-” in the same way we know “for ú·hav- use pen-”, which again brings us back to the avo nago solution.
I don’t know which criteria you use for crafting Neo-Elvish, but if you use a “later explanations beat the earlier ones” approach you are stuck with paradigm 2.
On the soft mutation of dag-: We have its past attested as aðanc, which supports your ú·dhag-, however usually the root is attested as NDAK-, which would make dag- a special case ⁿd- mutation (that’s why I used nag- as the soft mutation result above). It could however also be the case that dag- derives from an unstrengthened variant form DAK- (such a root exists in the EtymAC).
