I could make an argument for this either way. On the one hand, these spells "Make a melee attack with a weapon" which makes me think that it would not. On the other hand, from an action standpoint, it is clearly a spell and not an attack. Has this been settled?
Wand of the War Mage does not affect these spells.
"Spell attacks" and "weapon attacks" are mutually exclusive attack types (All attacks are one or the other, not both; See also), and the attacks made as part of these spells are melee weapon attacks; they use your normal attack stats/bonuses rather than your spell attack stats/bonuses, etc.
As such, effects that benefit spell attacks have no impact on the attacks for these spells.