It would be good to see a data comparison of cryptocurrency vs fiat and their perspective illegal activities. 1% will not be a big deal when we compare it with fiat money. With fiat, a huge percent of illegal activities is going on.
The research is already done by Messari, it turns out that fiat is used in illegal transactions much more often. 
https://www.ccn.com/fiat-money-outpaces-bitcoin-by-8001-for-nefarious-activities-report/
In my opinion, the reason bitcoin remains not so popular among criminals is transparency of blockchain and its ability to keep information about any activity forever. While cash transactions are barely trackable due to impossibility of recording numbers of all "taint" banknotes, bitcoin blockchain is always open and everything is recording by default. Despite the fact that there are many available methods to obfuscate transactions in bitcoin, all information is still open and forever written. As blockchain analysis methods are constantly being improved, it becomes possible to interpret past transactions.
thanks for posting this. I was looking for something similar regarding cash comparison to bitcoin regarding illegal activity. I would estimate a much higher % attributed for illagal activity using cash. Cash has no blockchain and is like bearer bonds imo.