Oh, I see.
That doesn't really work, though.
First of all, as a stand-alone you can only use such neuter pronouns in the nominative or accusative - in other cases it's not entirely clear which gender is meant and usually preference is given to the interpretation that you're talking about a person. This is also the case with your "cum aliquo lucter", which would translate to "I will wrestle with somebody", but not "with something". You usually need an addition in such cases, e.g. "cum aliqua re". With the "second" thing, I suppose you'd have to add something like
punctum or
momentum if you want to translate "second" literally.
The second little problem is that forms of
quisque are usually enclitic to superlatives, ordinal numbers, relative pronouns, reflexive pronouns or interrogative pronouns (SORRI) - although there are exceptions to this rule. With all of these lacking in the sentence you usually add the ordinal number yourself making it
unusquisque.
One more thing that's just come to my mind (because it sounded weird all the time): You use an ablative absolute and then continue with a pronoun refering to that ablative ... that kind of takes away its absolute nature, makes the sentence look strange and is not what the Romans did I think. If the participle can be linked to a part of the sentence, it's usually done as a participium coniunctum (e.g.
ei me neglegenti).
That would give you something like
ei me neglenti me (tamen) unoquoque puncto temporis dedo. Obviously, this sentence has the problem that the gender of
ei is not apparent anymore
To make this aspect, you probably have to use a subordinate clause rather than the elegant PC ... e.g.
cum illa me neglegat, me ei tamen unoquoque momento temporis dedo