Shadow Blade's description says:

It counts as a simple melee weapon with which you are proficient. It deals 2d8 psychic damage on a hit and has the finesse, light, and thrown properties (range 20/60).

Nothing more is said about the weapon's shape or type. Does it mean I get to decide when I conjure the weapon which shape I want it to take? Does it count as a Dagger (the only weapon that has all the aforementioned properties, besides the damage type)? Or do I simply not get any Mastery Property with it?
Thanks in advance :)

You simply don't get mastery properties. Mastery properties are properties of weapons similar to finesse, light, and thrown. The definition of mastery properties tells you that the weapon has the property, which means a weapon without such a property doesn't have that property.

I agree with @WolfOfTheBees. Shadow Blade doesn't have any Mastery Property.

Not exactly the same, but the topic was also discussed here: Shadow Blade Dual Wielded Bladesinger - Rules & Game Mechanics

Yeah I think that's fair. Shadow Blade is busted enough as it is already anyway :)

If you really want to spend one of your Weapon Masteries on a weapon you'll really only use for one minute, then summon again, I recommend Sap. It makes sense to me as the most generic sword (longsword) has that property, and it's not too strong.

There is miles of difference between "it counts as a simple melee weapon" vs "it counts as a simple melee weapon of your choice".

It doesn't become your choice of... anything. It just IS a: Simple. Melee. Weapon. And you're proficient with it. 

It is it's own thing.