I'm aware of the recommendation to avoid "strenuous exercise" for 24 hours. As a man, does this apply to sex?

Following botox treatment you shouldn't engage in any strenuous activity for 4 hours post botox and following that you can go on with your daily life activities including sex. 

You should be fine, there is really not much evidence that strenuous physical activity after Botox has any adverse effect. 

If there are any contraindications to sexual activity there are not Botox-related. For years many provider have recommended multiple restrictions after Botox injection - from not reclining to avoiding bending over. Yet, there has been no evidence ever presented that such restrictions are warranted or helpful. And there is always a magical timing of 4 hours attached to those restrictions. The last time I recommended those restrictions was 7 years ago; none since. Not a single problem.