If your strength training is sufficient quality then how can you achieve an hour of cardio? I've had sessions I can barely operate the car on the way home due to tiredness of muscles.
I would question the usefulness of any ST programme that you can complete an hour of cardio immediately afterwards.
Also, your muscles do like to have a small carb/protein snack after a good ST session within about an hour, so you're depriving yourself of that and the rest period for healing up when you exercise again immediately afterwards.
You're not doing yourself "harm". You're not exercising at your best, though.
Deb, in New Zealand