Can Snap Shot and Black Market Slicer both be used with the same pilot?

Yes. One is an EPT, one is an Illicit.

Does Snap Shot cancel out Black Market Slicer from be able to be used as well in that phase because that 'action' would be classed as an attack.

No. Attacks are two things:

Primary weapons

Upgrade cards with the Attack: header.

BMST is neither.

Does Snap Shot cancel out Black Market Slicer from be able to be used as well in that phase because that 'action' would be classed as an attack.

BMST is an action, not an attack. Just because you roll an attack die for it, doesn't make it an attack.

So you would activate your ship, reveal your dial, execute your manoeuvre, and if you're not stressed you perform an action, which might be BMST.

As Snap Shot isn't an action, you can't do that during your activation. But, when an enemy ship activates and executes a manoeuvre, you may trigger Snap Shot and make that attack. Be advised that Snap Shot is restricted to Range 1 and it is a secondary weapon, so it's also restricted to your primary firing arc only like any other secondary weapon attack. The fact that it doesn't take up a weapon slot, doesn't change the fact that it is a secondary weapon. It has the "Attack:" header, and that's what makes it a secondary weapon.

Rolling an attack die is in and of itself not an attack. So just because you roll an attack die with BMST doesn't mean you are in fact attacking.

Neither would Saboteur, Anti Pursuit Lasers or Ion Projectors, by the way, nor would R2-D2 (crew) be classified as an attack against yourself.

The earliest ruling that would deal with this is probably Stealth Device, which is discarded if hit by an attack. Seismic Charges and Asteroids, for instance, while requiring you to roll an attack die and apply damage, will not cause you to lose your Stealth Device.