There is a big difference between the bike and the stair climber as you can see. You would be the best person to determine the levels that are safe for your client. It is good to use both heart rate and RPE as you are doing. It is easy get winded on the stair climber as you are carrying your body upright against gravity.
You would need to consider your reasons for putting your client on the stairclimber, as well as making sure balance is good for that client. Taking everything into consideration and looking at the big picture of what you wish to accomplish will help guide you.