I broke my finger in a crash a few years ago in the late spring and had it in a cast up to my forearm. I tried to start training straight away and found it surprisingly difficult. Day to day the late spring/early summer meant it was always hot and sweaty. Add in training and it’s just…awful. I eventually settled on just accepting that it would be a maintenance break - anything beyond tempo (80-ish %) was just unpleasant, so it was a whole lot of endurance level work. I had the cast on for six weeks before it finally came off.
Baxter, West Vidette, Birch and, at a push, White, Mont Gosford and Mont Albert worked for me. Keep a fan on it and if you feel like sweat is getting too much, hold your arm up to let sweat drip down. You kind of have to accept that your cast is going to smell regardless of working out or not and, if you have a partner, hope that they can live with it. Luckily, mine was fine with it. It never got too awful as far as smell (or at least I never noticed. ) and training, even lightly, through it meant I could rebound back into harder workouts without too much difficulty after the cast came off.