IMO it's definitely a sexually motivated murder. Kate was stripped below the waist and the forensics certainly suggest a sexual element.
A dog isn't going to be a threat to an armed maniac, unless it's an aggressive Doberman, German Shepherd, Rottweiler etc. There was a similar case in the region where a man was scared off by an Alsatian IIRC. However, most dogs will cower or be no match for an aggressive man.
There are many cases where commuter offenders travel to quiet locations, and wait for lone females. I don't think it has to have been a local man.