No need for a lockpicker. You can always go back later after you've cleared the zone and get everything. If I recall correctly there aren't that many traps either, nothing too troublesome aside from some bear traps on the ground.
Two mages shouldn't be required to do this.
Shale has some interesting dialogue when you reach the end of the Deep Roads where you learn more about Shale's past. (My usual team was Shale, Oghren and then someone else to fill out whatever spot I wasn't). I'd try to keep the Golem and Oghren if you can. Usually I played an AW/SH mage, and did the Deep Roads third in the treaties, around level 14-15, as some of the mobs there can dish out a world of hurt. Alistair might come in handy depending on what level you are attempting this, and if you have invested in leveling his templar abilities (Smite) will help a lot against darkspawn casters. Or what is the mage spell, mana clash? if you have that. If you are attempting this too soon/low in the game, you may want to come back to it after doing some side quests or one of the other treaties first.
At the final moment, Oghren is forced into your group, so he's a 'must have' anyway, easier to just pick who you want to come with you all along, but the game will pause at the proper moment and you will have to rechoose your group if Oghren isn't with you, whereupon he is forced into it for the final conversation with Branka.
Talk to Shale, there are reasons the golem is very different from all other golems. The lore is "golems have been lost for a long, long time" (the reason Branka is in the deep roads is to find Caridin's anvil to make more of them), you would think it would create more of a fuss than the dwarves make over it, but sadly it doesn't. It could be there isn't a big hullabaloo over the golem in Orzammar because it was a DLC companion and while well integrated most times, maybe it was too much effort to change the reactions of the NPCs too drastically in Orzammar to cover that oddity in your traveling companions.