Is attending permissible worldly knowledge lessons considered a valid excuse for missing congregational prayer, or does sin befall the one who does so?

The preponderant opinion is that congregational prayer is obligatory. Therefore, you should strive to convince those in charge of the institution to give you an opportunity to perform it. If they do not agree, then join another institution if possible. If that is not feasible, then there is no blame upon you for not performing congregational prayer and praying after the lesson, provided that this does not cause the prayer to go out of its prescribed time. If it would cause the prayer to go out of its time, then there is no blame in combining prayers that are permissible to combine. It is not permissible to delay prayer beyond its prescribed time under any circumstances.