Spell sniper indicates that it gives all spell attacks double range. While "touch" does not have a range to double, I'm curious if attacking with a Shillelagh-ified weapon counts as a spell attack or a regular attack, since it uses your spell casting modifier for attack rolls and damage rolls. And if so, would that give the weapon reach?
Attacking with a weapon affected by shillelagh is a normal melee attack, not a spell attack. Shillelagh changes the ability used when making normal melee attack and damage rolls with the weapon, it doesn't make the weapon cast a spell every time it's swung.
Spell attacks are attacks made as part of the targeting of a spell. Those are the only attacks that Spell Sniper applies to. Also note that any spell attack that has a range of touch would not gain the reach property anyway, as doubling the range of "touch" is still "touch", not the adding of an unrelated weapon property.