I am not sure of an SQL-based approach, but you can use an ArcPy search cursor:
fc = # path to feature class
with arcpy.da.SearchCursor(fc, ["OID@","SHAPE@"]) as cur:
for oid, shape in cur:
if "curve" in shape.JSON:
I didn't realize your client was also stuck back at 9.3.x. Do you have access to a newer client that can connect to the 9.3 geodatabase?
If you have to stick with ArcGIS 9.3.1 as a client, I will have to think about options. It may be you could use comtypes or a similar package to access ArcObjects directly from Python.