Choosing a Warlock pact from one +1 and a cantrip from another +1 is not AL legal.
As a warlock (and not of the Tome), the only way you learn spells is either by selection at creation or upon advancing a level.
That you can only use materials from PHB+1 for creation-choices is well detailed in the first page of the Adventurers League Player's Guide. So you cannot, at creation, choose both Hexblade and booming blade.
Now flip to the last page of the ALPG, "Character Advancement."
Feats and spells gained by advancement are subject to PHB+1.
So you can't gain booming blade through advancement, either.
Note that spells copied into a spellbook do not fall victim to the +1 restriction, as they're neither gained at creation nor through advancement. But note further, that's a spellbook, not a grimiore