As you guessed, it is a futur proche dans le passé, or futur périphrastique au passé.

Using the present conditional would introduce a tense mispatch. To avoid it, you might have used the past conditional that way:

[…]sinon, nous aurions raté notre cours d’arithmétique.

However, this introduces a slight change in meaning because that sentence states the lecture wasn’t missed, an information the original sentence doesn’t assert.

Using the imperfect is a possible alternative:

[…]sinon, nous rations notre cours d’arithmétique.