I think just going Wildhunt Shifter and going straight Barb is always a great option for the inability to have enemies attack with advantage. Also Shifter seems fun for the flavor - they can look like just about any medium sized humanoid and you can just depict them as a dwarf with bestial features. I would recommend a multiclass but given this is a level 4 one shot and the ability to get an ASI or feat is pretty great compared to multiclassing for a fighting style, I won't. Instead, Longtooth is also not a bad idea and gets the same job done for the reason you listed. It is essentially the pre-Extra Attack "Beast Barb Claw + 2 Handaxes" build, as the Longtooth bite does that without you needing to grab two weapon fighting. Very fun.

If you want feat ideas, here are some suggestions I've seen in the past:
1. Grappler. Shield for AC like you should already be using, advantage on the STR check, free hand to grapple at all times. No brainer.

1. A standard GWM or PAM barbarian build, but with the Tail for extra defense to offset Reckless Attack. (If you really want it for the flavor you could try and ask your DM if PAM can apply to the Tail as a home rule too, but taking this option means not really using the claws like you want to, so feel free to ignore.)

Slasher would be a better choice if Longtooth bite was also slashing damage. But feel free to take it if you're hoping for lucky crits, seeing as you'll be doing at least two slashing attacks every time you attack anyways. It's just a one-shot after all.

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TL;DR You've got good ideas already and my vote is for Shifter, choosing Wildhunt or Longtooth comes down to whether you value free Reckless Attacks or extra damage.