Hmm, well he isn`t a psyker at all, I don`t believe.
Not inherently a problem but probably not something to pursue. The Dark Heresy and Deathwatch psyker mechanics are fundamentally different so it's best not to provide the opportunity for overlap.
Stormtrooper does work fairly well - not for firepower, although it's not as bad as you think:
Against an armoured target a stormtrooper's hellgun is only 3 points of damage short of a godywn-pattern bolter, and he can trade up to military plasma weapons or stormbolters fairly easily.
More important, though, is his ability to requisition dudes with Influence - a small horde of stormtroopers and a commander (see the Oblivion's Edge ) is a nice force in Deathwatch, and works well as a 'player character' in combat.
Lastly, he's likely to be 'all things to all men' - the Heed The Higher Call stormtrooper starts with Command, Drive (All), Pilot (Flyers), Demolitions, Medicae, Tech-Use, and Security - all skills which can be extremely valuable to a kill-team in a combat zone if not in combat directly.
Provided you're not facing the fire of hordes directly, he's not too bad durability-wise, either; toughness is ~50-60 (depending on homeworld and where you spend stats), with 7 points of armour and - more importantly - agility nearly as good, Dodge +20 and Step Aside.
By allowing him access to cheaper weapons, do you mean the weapons listed in the Deathwatch CRB or the weapons listed in DH Ascension?
I'd stick to DH weapons (including Ascension ones). If you're going to use a non-astartes, it's worth underscoring the difference in their calibre of armament, which would be heavy weapons for a 'mere mortal'. If you really want to prove a point, you could let him have an Angelus Bolt Carbine from the Inquisitor's Handbook . Essentially firing Astartes bolt rounds (you might want to update the stats to match), but Accurate and (sadly) with only three rounds fitting in a clip!