Present tense use of pouvoir
The present tense is completely fine and idiomatic:
Bien sûr, je peux !
Je peux le faire.
Demain, je ne peux pas.
In the negative, it can even be made to sound more colloquial by omitting the “ne”:
Demain, je peux pas.
It's omitting the “pas” that sounds stiff and formal:
Je ne peux le faire.
Or even worse but still correct:
Demain, je ne peux.
And of course:
Demain, je ne puis.
(Actually, I have difficulties imagining myself uttering “demain, je ne puis” without some pompous tone and hand gesture to go with it!)
The special case of “aucun”
But in a sentence like yours (“I can't find it in any dictionary”), you cannot fit a “pas” so if you want to keep the present tense you have to say
Je ne peux le trouver dans aucun dictionnaire.
and, while it's already much better than “je ne puis”, it stills sounds a bit like “je ne peux”, whereas
*Je ne peux pas le trouver dans aucun dictionnaire.
sounds childish or downright incorrect.
Getting rid of “pouvoir” entirely makes the sentence feel less formal, even without “pas”:
Je ne l'ai trouvé dans aucun dictionnaire. [My original suggestion]
Je ne le trouve dans aucun dictionnaire. [Suggestion from @undu]
Past tense and “je n'ai [pas] pu”
On its own, “je n'ai pas pu” also sounds fine but I suspect that it's not because of the past tense but because of the “pas”. And of course, it's just as difficult to use in a sentence with “aucun” as
*Je n'ai pas pu le trouver dans aucun dictionnaire
is also incorrect. While
Je n'ai pu le trouver dans aucun dictionnaire
suffers from the same undertones as the present tense version and still feels quite formal.
Conclusion
Depending on what you are trying to say, it might or might not be possible to construct a present tense sentence that fits the situation but there are certainly many uses of “peux” in informal settings.