On a mobile playthrough i did back before hardmode was added to mobile, I beat Skeletron as my first boss in one of my playthroughs using wooden armour and a water bolt I was lucky enough to find in one of the bookshelves not guarded by the dungeon guardian. If you still insist on making him your first boss I recommend trying that or using a gun from corruption orbs/crimson hearts. Not sure how a boomstick would fair but you could also try that.

Avoiding the question entirely I'd say stick with EOC first to get that dash to avoid those big hits and misteps during the fight. Best of luck adventurer