D&D 3.5e isn't historically representative.
If you look at the picture of the swords in the Player's Handbook, you will find that the longsword is actually a picture of a bastard sword, the bastard sword is actually a picture of a longsword and the greatsword is actually a zweihander. There were no "greatswords" per se, it was just a generalization for D&D to classify big long heavy sword that requires two hands.
The bastard sword, or hand and a half sword, had a standard grip for one hand, but also tapered at the bottom with a hefty pommel that could be gripped by the second hand. If you look, once again at the Player's Handbook, that is the photo used by the longsword.
The longsword, historically, was not a one handed blade. The handle grip was designed for two hands. It was a lot lighter and more mobile than the two-handed sword.
When it comes to one handed swords, once again it is a generalization. The Anglo-Saxon Seax wasn't primarily a stabbing (piercing weapon). It was an edged weapon (slashing) and it has been noted as such due to the lack of handguard. Handguards, not only helped protect the fingers from another attack, but also prevented your hand from sliding up the blade when stabbing.
Look at this "short sword" (seax) from Owen Bush. There is very little to stop your hand from sliding off the grip if a stab is made. That would make stabbing with it less likely. Could you stab? Sure, why not. Is it optimal? No.
Look at this "short sword" (gladius) from Cult of Athena. There is a very pronounced handguard to prevent your hand from sliding forward. Also look at the very prominent piercing tip. That would make slicing with it less likely. Could you slice? Sure, why not. Is it optimal? No.
Reading the short swords description in the Player's Handbook will reveal that it is often used as an off-hand weapon. Due to the piercing nature and the european influence of D&D, the short sword in the player's handbook is most likely modeled after a main gauche.
Look at this main gauche from True Swords. It is a little longer than the typical dagger, with a very very deliberate pointed tip. Main gauches, in historical fencing, were designed to parry and stab in conjunction with a rapier, foil, epee, etc.
The wakizashi, in Oriental Adventures, is listed as having the same characteristics as a masterwork short sword. However, wakizashis were made along with and with similar techniques as the katana. One doesn't need to go far to see the cutting tests with the katana.
Look at this wakizashi from Casiberia. The wakizashi has the slight bend to the blade, emphasizing a cutting edge, rather than a piercing tip. Can you pierce with a wakizashi? Of course. Will it slice better? Absolutely.
Use Houserules for alternatives.
Wanting a thrusting short sword? Style it as a gladius. Want a slashing shortsword? Style it as a seax. Your culture and region of play in-game will determine what weapons are available, in use, and how they are used.
No, it doesn't work.
But with the Weapon Versatility feat (requires Weapon Focus) from the Undead Slayer's Handbook, you can use the Estoc with Slashing Grace just fine.
Benefit: When wielding a weapon with which you have Weapon Focus, you can shift your grip as a swift action so that your weapon deals bludgeoning, piercing, or slashing damage instead of the damage type normally dealt by that weapon. You may switch back to the weapon’s normal damage type or another damage type as a swift action. If your base attack bonus is +5 or higher, using this feat is a free action instead.
However, there are other options that you can look into:
Mythic Weapon Finesse - only available if you have mythic. Allows the character to add dex to damage to all finessable weapons.
4th level of a swashbuckler archetype called Whirling Dervish. This applies to all weapons that work with Swashbuckler finesse plus scimitars.
At 1st level, a swashbuckler gains the benefits of the Weapon Finesse feat with light or one-handed piercing melee weapons, and she can use her Charisma score in place of Intelligence as a prerequisite for combat feats. This ability counts as having the Weapon Finesse feat for purposes of meeting feat prerequisites.
- 3rd level of Unchained Rogue (and again at 11th and 19th levels) allows one to select a single finessable type of weapon so you can use dex to damage with that type of weapon.
Finally, if the Path of War from Dreamscarred Press (third party publisher) is allowed, you have Deadly Agility, which allows you to use dex to damage on any light or finessable weapon.
Best Answer
There is no existing way to do it in the rules.
There might be ways that exist but if they do they are so obscure (splatbook feats from 3e for unarmed-strike only) that you might as well just houserule.
-4 is a good basis, because that is the same penalty as using an improvised weapon.
Change Weapon Damage, (Houserule)
By taking a -4 to hit, you may do a different damage type with a weapon than it normally does. Cutting with the blade of a rapier, bashing with the hilt of a longsword, you may change your damage type to one of; bludgeoning, slashing, or piercing for that one attack. You may change weapon damage types on any attack, even one which is part of a Full Attack action, or a Charge.
Class features or feats that specify a damage type ('a slashing weapon' etc) will not function if you use 'Change Weapon Damage' to change the damage type to a different one than the one mentioned in the class feature or feat.