You could store the blaze's health value before the snowball hits him, increment it by the amount of damage the snowball does and then store it back.
/scoreboard objectives add snowballDamage dummy
/scoreboard objectives add health dummy
/scoreboard players set snowball snowballDamage <damage_amount> (fill in the amount of damage the snowball does)
/execute as @e[type=snowball] at @s run tag @e[type=blaze,distance=..5] add modify
/execute as @e[tag=modify] run execute store result score @s health run data get entity @s Health
/execute as @e[tag=modify] run scoreboard players operation @s health += snowball snowballDamage
/execute as @e[tag=modify] run execute store result entity @s Health double 1 run scoreboard players get @s health
/tag @e[tag=modfiy] remove modify
adjust the distance from ..5 to something larger in case the snowball hits him before the tag is added.
(You don't have to use "/execute as..." for the storing but I use it anyway because it's easier to get a reference to the entity)