Is there anyway to build a blue laser driver circuit WITHOUT using a LM317 Chip?

No. you need that regulator to accuratly measure the current or you will destroy the laser diode . Blue laser Diodes will Blow on regular 3 volt batteries because a regular battery (aaa) supplies way more current to the diodes than it needs thus burning it out .Most AA batteries can produce 1 amp or more . (Poof)