It's not so much about if the words are suitable for this specific situation but more about the combination of the adjective and the word situation.
(In this case something had forgotten his watch he would have needed.)
Is it in general possible to combine the two adjectives with the word situation?
As far as I know, both are possible, though quite informal. I'd say 'stupid situation' more frequently than 'silly'. If I wanted it a little more formal or a a bit stronger I'd say something like 'ridiculous situation'.