INT doesn't necessarily boost only SWoT's damage. It boosts all Critical damage and since SWoT can increase it's Crit and has two strong attacks that have 100% to Crit, INT is preferred for that class.
So what you need to know about the stats are the following:
Mainstat for Melee attacks
Increases base damage of Melee hits by STR/10, rounding down
Increases damage of all non-critical hits and glancing critical hits by (STR/10)% (+20% at 200 STR)
Mainstat for Pierce attacks
Increases base damage of Pierce hits by DEX/10, rounding down
Increases damage of all hits by (DEX/40)% (+5% at 200 DEX)
Increases DoT damage by (DEX/4)% (+50% at 200 DEX), capped at 400 DEX (+100%)
Mainstat for Magic attacks
Increases base damage of Magic hits by INT/10, rounding down
Increases damage of all critical hits by (INT/10)%, additive (+0.2x critical damage at 200 INT)
Most classes have a base critical hit modifier of 1.75x, increased to 1.95x with 200 INT
Very few of the classes are locked to specific stat. But to answer your question, if your weapons' type are scythes, you can train INT and it will benefit them. As Scythes are not locked to specific weapon type can use any of the three stats freely (where as Axes/Swords are Melee type, Wands/Staffs are Magic and Daggers are Pierce).
And if you have trained INT but are using melee weapon, it will still increase your critical damage, but not your base damage.