The following standards and specifications may be useful to you:
ISO 13919-1 WELDING - ELECTRON AND LASER-BEAM WELDED JOINTS - GUIDANCE ON QUALITY LEVELS FOR IMPERFECTIONS - PART 1: STEEL
ISO 13919-2 WELDING - ELECTRON AND LASER BEAM WELDED JOINTS - GUIDANCE ON QUALITY LEVELS FOR IMPERFECTIONS - PART 2: ALUMINIUM AND ITS WELDABLE ALLOYS
ISO 15614-11 SPECIFICATION AND QUALIFICATION OF WELDING PROCEDURES FOR METALLIC MATERIALS - WELDING PROCEDURE TEST - PART 11: ELECTRON AND LASER BEAM WELDING
ISO 9956-11 SPECIFICATION AND APPROVAL OF WELDING PROCEDURES FOR METALLIC MATERIALS - PART 11: WELDING PROCEDURE SPECIFICATION FOR LASER BEAM WELDING
ISO standards are available from ISO at
or from Global Engineering Documents at
SAE AS7110 National Aerospace and Defense Contractors Accreditation Program Requirements for Laser Welding
You can obtain this standard from SAE at
AWS C7.2:1999 Recommended Practices for Laser Beam Welding, Cutting and Drilling
AWS B2.1:2000 Specification for Welding Procedure and Performance Qualification
You can obtain these codes at
I could not find any MIL or ASTM specs that cover laser welding.