You can smite divinely while enraged.
There's no spell named divine smite; you're not casting a spell when you use that class feature. It's a feature triggered when you hit with a weapon attack.
This, by the way, is another way you know it's not casting a spell: you're (most-likely) taking the Attack action to make your melee weapon attack, rather than the Cast A Spell action. It's rare--and explicitly spelled-out circumstances--where you'd make an attack but end up casting a spell.
Ideally, Sacred Flame kills it (roughly) twice as fast
A simple formula answers this, with X being the number of rounds needed to kill the Shadow.
1d10 averages 5.5, halved is 2.75
1d8 averages 4.5, doubled is 9
For Firebolt, you hit on 8-20 (chance for crit), so .65 x (5.5/2)(crit bonus)x(XFB) >= 16
(Need to hit AC 12; roll 1d20 +2 Int +2 proficiency)
(14 / 13 = crit factor; (x+1)/x for damage with the chance of crit thrown in)
For Sacred Flame, you hit on 13-20 (and no crit) .4 x (4.5 x 2)(XSF) >= 16
With a DC of 11 (you only have +1 due to your 12 Wisdom)
(The Shadow makes a dex saving throw versus the spell)
Solve for XFB: 16/(.65 x 2.75 x 1.077) = 8.31 rounds
Solve for XSF: 16/(.4 x 9) = 4.44 rounds
As a practical matter, being able to kill it in ~4 rounds rather than ~8 rounds means that your Sorcerer with that meager 16 HP has a far better chance to survive the fight before having no offensive capability.
Actions
Strength Drain. Melee Weapon Attack: +4 to hit, reach 5 ft., one creature.
Hit: 9 (2d6 + 2) necrotic damage.
Two hits and your Sorcerer is down.
This is an encounter were the Cleric's "turn undead" would be a handy skill to have.
This whole problem also presumes that you stay more than five feet away from the Shadow. In the case of firebolt, since that is a ranged spell attack rather than a spell that calls for a save, if the Shadow closes to melee range your firebolt attacks at disadvantage.
(SRD p. 103; spell attacks) Most spells that require attack rolls involve ranged attacks. Remember that you have disadvantage on a ranged attack roll if you are within 5 feet of a hostile creature that can see you and that isn’t incapacitated.
Best Answer
From What are the most common damage types per spell level?, there are 14 spells that deal radiant damage, making it the 5th most common spell damage type. These are predominately cleric and paladin spells. There is at least one for every spell level except 7th and 9th so they are available early and often. Radiant damage is a good choice because few creatures are resistant or immune to this type of damage unlike, say, fire which is both the most common spell damage type and the most resisted.
That said, your question is highly dependent on how you use undead in your game. If the players never fight them then obviously it will have no effect whatsoever. If the campaign is a zombie apocalypse and that's all they fight then it will have a much greater effect. How much you telegraph what they will be facing will also be a big factor - clerics and paladins with foreknowledge can optimise their spell selection. If this telegraphing extends to pre-character creation then players may be drawn to paladin and light-domain clerics, this is not necessarily a bad thing.
As to the effect of vulnerability on CR the DMG has this to say (p. 277):
This makes sense, if 1 (or 2) PCs in a party of 4 do double damage on a successful hit the effect is as if there was 1 (or 2) more PCs making attacks but there are still only 4 copping damage. The creatures will be down 1/4 to 1/2 as quick but most creatures hand out the bulk of their damage in the first couple of rounds anyway.
Of course, you are the DM, if you slip 1 more zombie into the pack or give the lich 25% more hp the effect of radiant vulnerability will be effectively cancelled out but the PC who picked paladin still gets to feel clever.