Error You do not have sufficient permission to transfer/cancel this participant
Jason, Welcome to stackexchange. Sorry for the problem you facing. There is no specific permission required to cancel your registration and neither the user should be logged in. However the url should have correct parameter i.e contact checksum. eg 

http://www.domain.org/civicrm/event/selfsvcupdate?reset=1&amp;pid=53&amp;cs=7f51ab615c6bdcb785d1947e122b1c14_1548964126_inf


If the cs is invalid then you will get above error. So please check if the url is correct and hopefully not encoded.

HTH

Pradeep