I know it feels odd. I'm just arguing RAW here, and that has nothing to do with how I feel about the situation.
A quick houserule can end the discussion pretty quickly in any case.
As TJ said, a popular way to rule exotic weapons is to allow specializations, in this case into your natural spiky tail, which could, in turn, qualify for that particular MA.
Also, something that struck me, from your OP:
QUOTE
Are spurs "blades" at all? You roll the test with cyber implant weapons.
You don't roll with the skill cyber implant weapons. You roll depending on the implanted weapon, e.g. blades skill for spurs, unarmed skill for hand razors, and so on.
Cyber implant weapons is a specialization of these skills.
QUOTE (SR4 Core Rulebook @ p. 122, "Blades")
This skill is used for cyber-blades implanted in the hands or forearms, but not other areas of the body.
QUOTE (SR4 Core Rulebook @ p. 122, "Unarmed Combat")
In addition to Boxing, this skill covers such combat styles as Oriental martial arts and Brazilian Capoeira. It also covers the use of certain cyber-implants, such as shock hands.
It's not clear if hand razors are blades or unarmed, btw, since the equipment section doesn't define it. So, YMMV.