[RPG] Does Smite work while wild-shaped

I would recommend starting with a race that provides a Wis bonus and a bonus to Con or Dex, so Elf, Dwarf, Razorclaw Shifters, Githzerai and Wilden of the various PHB races.

Using an array of 15, 15, 15, 11, 10, 8 for stats you can get Wis and either Con or Dex to 17, and then Str and the other get 15 and 11, giving you a pretty beefy 17, 15, 11 in your physical ability scores, and still retaining a 17 Wis.

Unfortunately Driuds lack at-will powers with secondary stat kickers, so your secondary stats being high isn't as much of a win as it is for many other classes.

The starting -2 to hit that you suffer against the pre-racial adjusted 18 wisdom druid can be mitigated first by taking implement/versatile expertise, superior implement training-accurate staff, and also your odd number in wisdom means that a level 4 attribute boost to wisdom gives you a +1 to hit.

Yes, the Savage Attacks ability will work while Wild Shaped. Wild Shape allows you to use your racial features:

You retain the benefit of any features from your class, race, or other source and can use them if your new form is physically capable of doing so.

Savage Attacks kicks in when you get a critical hit with a melee weapon attack:

Savage Attacks. When you score a critical hit with a melee weapon attack, you can roll one of the weapon's damage dice one additional time and add it to the extra damage of the critical hit.

Every beast type creature that I can think of has at least one attack that is a melee weapon attack. For example, the Wolf:

Bite. Melee Weapon Attack: +4 to hit, reach 5 ft., one target. Hit: 7 (2d4 + 2) piercing damage. If the target is a creature, it must succeed on a DC 11 Strength saving throw or be knocked prone.

So if you get a critical hit while Wild Shaped into a Wolf, it will deal 5d4 instead of 4d4.