- scimitar shouldn't be offhand.
Rapier can be and is used dual - even up to 4' blades (I've done 3.5 in one hand and 4' in the other many times - usually with the long in the off-hand.). The term is «case of rapier» in the period manuals.
There are comparable scimitars for heavy-blade fencers (rapier, triple epee, dimond schlaeger), and I assure you, the 3.5' ones can be used paired. It's not as natural as case of rapier, but it's just as doable.
It naturally falls, as does case of rapier to the same shifting of offense blade and defense blade back and forth; a fencer of paired rapier who learns the technique differences for single scimitar can easily convert to paired scimitar. (Also, historic scimitars are not the wide ones of Hollywood fame... the term shamshir is
almost synonymous - and single hand shamsheers to over 4' blades are known. (A mamluke hilt of 8" isn't big enough for two-hand use.)
If you can wield one whatever 1 handed, you can wield two of them at once. Basic knowledge of almost every ARMA fighter, SCA fencer, and SCA Heavy...
Most of us also learn that, most of the time, a shield is better than an off hand dagger... but an off-hand longsword is
almost as good as a shield, and less tiring, plus adds many more options for feints.
Now, dual shield isn't allowed in ARMA nor SCA, not because it's ineffective, but because it's not able to be safe to use a shield offensively without serious risk of injury to the target. Shield punches can easily break ribs and dent breastplates.
@Jd Smith1 the difference between a fencing dagger and a short sword isn't much - the range of hilts for fencing period daggers (15th to 17th C) vary widely, from my preference of quarter sphere solid through simple Scots dirk spool, and is the same as the range for shortswords. That's also most of the Reiver period in Britain. Length and edge placement determine use type within each system; a dirk, often made from a broken longsword, would be 12-18" and in a spool hilt. Since Scots longswords were usually basket hilt, single or half-double edge, and equipped with a thrusting point... so were the dirks, tho' some wound up thus being fully backedged.
As for the differences between dagger, knife, and short sword, really, they're a spectrum, not discretely different types.
They're all pointy, all have at least one sharp edge, and can have anywhere from dirk-style spool to full basket hilt. (The technical distinction between knife and dagger is 1 vs 2 edge
in modern parlance. But that's due to modern classification systems, not period understanding.)