You don't need HRM to get a blue badge. HRM is just a 'passport' to a blue badge.
If you can show that your DS meets the other criteria for a blue badge, then you can apply for one on that basis.
Also, don't be fooled by their 'physically unable to walk' criteria if your child's problems with walking are a lack of danger awareness, behaviour, or stumbles, trips and falls:
If your child has a brain condition (including ASD, which is accepted legally to be an 'organic' condition) you can say that it is the physical variation in the brain which is resulting in behavioural difficulties/no sense of danger/stumbles trips or falls.
If a person had difficulty walking because of damage to their back which caused them to stumble/trip/fall or experience pain on walking, they would still qualify despite their legs being perfectly functional. Similarly, if your child's brain is damaged or altered and this results in difficulties with walking, despite their legs being perfectly functional, your child should also qualify.
DD1 was refused a blue badge and I appealed (successfully) on these grounds. She was awarded HRM a few months later.