There are two primary issues here, carbon and plastics.
I would expect carbon emissions to be higher for ink, but not significantly. Transport/logistics/retail would be similar for both products and likely has higher emissions than manufacturing.
Modern Ink usually includes micro plastics within the ink, and the packaging for a pen refill also has much more ...
According to Wikipedia:
Propane is produced as a by-product of two other processes, natural gas processing and petroleum refining.
The amount from petroleum refining is minimal. The U.S. Energy Information Agency provides detail about how much propane (a hydrocarbon gas liquid) is produced by each source:
Continuing from Wikipedia, if propane wasn't ...