I wouldn't take Wiktionary's declension tables too seriously. They're algorithmically generated, and don't necessarily imply that any particular form is attested.
In this case, I haven't been able to find any attested forms apart from the tuditēs and tudibus you cited. So any singular forms would have to be back-derived from there.
The genitive singular is nice and easy to predict: we can cut off the plural endings to get the stems tudit- and tud-, then add the third-declension -is, to get *tuditis and *tudis. This is what L&S have done. All plural forms and most singular forms are built off the same "apparent stem", whether or not it's the same as the underlying stem, since all those endings "react" the same way.
The nominative singular is a bit more difficult. On the face of it, we would expect to just put the third-declension ending -s on the end of the stem, then apply regular sound-change laws: *tudit-s > *tudīs > *tudis (cf lapid-s > lapīs > lapis "stone", nom pl lapidēs), or *tud-s > *tūs (cf ped-s > pēs "foot", dat pl pedibus).
However, due to vowel reduction, we can't actually be certain of the vowel in the stem: it's also possible the original stem was *tudet-, which would give a nominative singular *tudēs > *tudes, but the same plural *tudet-ēs > tuditēs (cf milet-s > milēs > miles "soldier", nom pl militēs).
Or, instead of ending in a consonant, this word could have been an i-stem *tudi-, in which case the nominative would be either *tudis or *tudēs, but have the same plural *tudi-ibus > tudibus (cf vāti-s > vātis/vātēs "bard", dat pl vātibus).
L&S seem to have considered the form *tudes and/or *tudēs the most reasonable (conveniently leaving off the vowel length), and chosen it as their reconstruction. Which makes sense to me: nouns declining like vātēs and miles are significantly more common in Latin than nouns declining like pēs or lapis. Moreover, it would explain how we see both tuditēs and tudibus: it was presumably an obscure word, so an alternation between *tudes and *tudēs isn't too far-fetched (especially since we see this sort of vowel alternation in better-attested third-declension nouns too). Some people used it one way and ended up with tuditēs, some used the other way and ended up with tudibus, and the word as a whole ended up with two different declension patterns. (However, I'd still have marked it with a star, personally.)
As for the short ŭ in the stem, I'm guessing that's for etymological reasons. Compare tutŭdī "I have hit", stŭdeō "I dedicate myself to". This noun seems to have come from the same root, and would be expected to have the same vowel quantity.