No, you don't need one.
Check 23.8 for required equipment.
https://www.tdisdi.com/wp-content/uploads/files/sandp/currentYear/SDI/part 3/pdf/individual/SDI Specialty Standards_23_Solo_Diver.pdf
Okay, then a Spare Air, or another fully redundant air source of which for single tank diver a pony is the most practical.
Required Equipment
Basic open water scuba equipment as described in section three of this manual with exception of a safe second, or octopus, is not allowed as a redundant air source.
One of the following must be used to provide an additional independent regulator attached to an air source: pony cylinder, twin cylinders with isolation, H-valve, independent doubles, or SpareAirTM
N