If the oil you put on the strop made the strop work wonderfully well for you, well... that's wonderful. It's certainly not going to rust the leather. On the other hand, the oil you used to treat the strop may not be a corrosion inhibitor for the razor. You could do a control test with some of that oil slathered on a none razor piece of shiny high carbon steel. Let it sit around for a while to see if it proves hygroscopic and encourages rust or, hopefully, proves to be a rust preventive as well as a strop dressing.
good luck, good stropping,