You could use paper towels, but I wouldn't use just paper towels. Instead, use the paper towels to remove the larger debris and sediment and then go back and use coffee filters. Unbleached coffee filters are healthiest to use.
What happens if you don't straing at all? You get sediment, organic compounds and don't remove enough of the cardiac glycosides. Very likely you will have problems with nausea and diarrhea and perhaps worse.
The instructions are there for a reason and should be followed precisely.