Valor is the better option
"Cast and slash" in the same turn is basically impossible before Battle Magic, and far from powerful even then.
"Cast one turn, slash next" is possible, but suboptimal, as one of them would need Charisma, the other Dexterity, you would need different feats and magic items. You should pick one or the other, and focus on that.
If you want to be good with melee weapon attacks, you should go with Valor, unless you can get Extra Attack from 5 levels of Fighter, Monk, Paladin, Ranger or Bladelock. You said multiclassing might be impossible, so Valor is basically the only option for a fencer.
If you are fine with using spells instead of weapons, a Lore Bard might be viable. Unfortunately bard cantrips from PHB are mostly bad in combat.
Thunderclap from Elemental Evil is nice, especially if you can get more than one enemy with it, but it is unsuited for stealth missions.
Vicious Mockery's disadvantage becomes inefficient when most enemies get multiattack, and the damage is ridiculous even before that.
A Magic Initiate feat can fix that, or you can spend Additional Magical Secrets for getting a worthwhile cantrip. I suggest Acid Splash if you expect more than one enemy to receive it, Shocking Grasp if not, and Thorn Whip if you use Additional Magical Secrets.
In the front line you will need AC. As you lack the Strength for Heavy Armor, not even multiclass will help you with it. The shield is your best friend. Valor gets it for free on level 3, but Lore needs to pay another feat, fortunately it increases Dex as well. Either way you get Expertise, if you put it on Athletics, you can provide near constant Advantage for you melee party members with Shield Master.
Comparing the two options on level 8:
level 4: +2 Dex
level 8: +2 Dex
AC: 19 (Studded, Shield, 20 Dex)
Attack: +8 (weapon)
Damage: 2x 1d8+5 (Rapier)
DPRvs16: 12.35 (19 x 0.65)
Casting: Cha 17, has to drop weapon for spells
level 4: Moderately Armored
level 8: +1 Dex, +1 Cha
AC: 18 (Studded, Shield, 18 Dex)
Attack: +7 (both with cantrips and weapons)
Damage: 2d8 (Shocking Grasp)
DPRvs16: 5.6 (9 x 0.6)
Casting: Cha 18, right hand empty
So in combat prowess Valor is clearly superior, while only a tiny bit weaker as a caster (spell DC 14 vs DC 15). Even on level 17, Shocking Grasp will do only 18 damage, compared to 19 with a Rapier.
To sum it up, if you want to stay alive and relevant in the front line, Valor gives you the defense and the offense.
You don't need multiclassing
Starting as Fighter and then changing to Lore bard would be great, as it gave you heavy armor, but you lack the Strength for those.
A Valor bard does not really benefit from multiclassing (probably a few levels of Rogue for DPR).
If you do not want to be melee: Your party can get by with only two melee characters, and bards perform much better in the second line.
- Go Lore, get a good cantrip, meaning Eldritch Blast through multiclassing or the feat Magic Initiate, and you will be optimized enough.
- Go Valor with a Hand Crossbow, Crossbow Master and Sharpshooter. Huge amounts of damage, spells only for Advantage and utility.
If you can multiclass, change your race and ability scores: 1 level of Fighter, continue in Lore bard. Swap Dexterity and Strength. In heavy armor AC costs money, not attributes, and you will always have more money than Ability Score Improvements. Second Wind is great at low levels. Fighting Styles are good too.