Item for any class: flip shoes. After jumping, you can double-jump to do a backflip, much in the style of Richter Belmont. (For Scouts, the backflip activates by jumping after doing a double-jump) It gains you a very small amount of altitude, but the main thing is that it sends you backwards faster than you can run, conveniently escaping melee range with naught but a double-tap of the ol' spaced bar. Not intended to be a viable alternative to anything.
Spy sapper replacement: electromagnet. It disables buildings from a pretty good range, has a conical area of effect, and does more damage than a regular sapper, but the damage lasts only as long as you are using it, and the disability only lasts for a second or two longer (long enough to backstab then switch back and finish the job, say). You can move around while using it, but not as quickly as normal. Point it at ammo boxes and dropped weapons to draw them towards you. To defend his buildings, the Engineer must kill you, rather than giving him the illusion that knocking the sapper off will accomplish anything. This vulnerability is the counter to its increased ability to sap.
Heavy buff: when spun up, very nearby ammo is similarly slowly drawn towards the Heavy.
Spy needs a custom animation for when you suicide via console or class-switching, wherein he takes a cyanide capsule.
Bat replacement: Bonkscalibur, the legendary baseball bat of King "Babe Ruth" Arthur, or some other ridiculous portmanteau of a legendary sword and a legendary baseball player. This is the weapon of an honorable warrior, and it cannot be returned to its sheath without first having drawn blood. Does more damage (either it does damage as if it were another class' default melee weapon, or regular hits become mini-crits against enemies with melee weapons out, or something), but if you miss, it does damage to the user equivalent to the damage of a normal aluminum bat hit. You cannot switch to another weapon until you have hit either an opponent or yourself. (This limitation does not apply if you have the weapon out for less than a full second without attacking) It is possible to kill yourself in this way, and an achievement should be associated with it.
Revolver replacement: poison dart gun. Slow to reload and always does exactly one point of damage, but its hallucinogenic projectiles (which travel at about the speed and arc of the needle gun) send the enemy into the "panic" state (can't fire) for one second, or three seconds on a crit. Single action like the flare gun; the reload time should be such that you can just barely keep firing on an enemy to keep them afraid of you.
Medigun replacement: healing laser. A conical area of effect gives health to all allies within it. It must be aimed and heals single allies more slowly than the regular medigun, but can heal multiple allies. Ubercharge: all living allies and the user instantly reach maximum overheal, and the overheal doesn't decay for ten seconds. Allies who respawn during those ten seconds spawn with this buff applied as well.