Smart call taking a day off the feet. Doing a workout on the bike is a great alternative. HR zone values do tend to be slightly different for different sports. Cycling zones are often ~10BPM lower than running. I think the main thing is to aim for that perceived effort of Z4 (in this workout's case) and the HR isn't as important. In an ideal world, it's nice to be able to do zone tests for cycling and running but it's not critical.
Oh, I didn't know that about different zones for different sports. Thanks!