Teleporter replacement: emergency exit. An ally can step on one of these platforms, but it won't immediately do anything; afterwards, before dying, they can press the "drop intel" key to teleport back to it (immediately or as soon as it finishes recharging). The teleport leads to the last one used in this life, and obviously you can't use it without first stepping on it. This doesn't help allies get to the objective faster, but it helps them stay alive and fighting on hectic fronts, makes it easier for them to help protect a forward base, and sets up for absurdly complex strategies (especially for defense) on maps that have multiple unlocked points.
Dispenser replacement: Engiebot. This (not-very-)lifelike animatronic Engineer can be planted on top of an existing building for only 75 metal, and will automatically (albeit slowly) upgrade it to full capacity and repair it if damaged, even if you're dead. It will also, if placed on a sentry or a fellow Engineer's dispenser, kill any enemy foolish enough to stand directly on top of it, but this is more of an easter egg. Engiebot has little health and cannot itself be repaired or upgraded, but it will protect the building it's built on from sappers. Specifically: the sapper will go on the Engiebot instead of the building below, even if the Engiebot is already sapped. Engiebot will heal and resupply nearby allies significantly slower than a dispenser, and while it is doing so, it will not repair the building it is built on. And no, you cannot place an Engiebot on another Engiebot.
Dispenser replacement: field supplies. Straight-up boring alternative: refills and heals much, much faster than a regular dispenser, but has a finite supply of both and will break when it runs out. Give it a whack to refill it, leading to paradoxical infinite metal scenarios, but requires constant attention.
Sentry replacement: Artillery. Fires powerful arcing grenades constantly and with only minimal aiming at various trajectories within a quarter- or eighth-circle range.
Pistol replacement: Binoculars. Takes three seconds to charge up once you pull 'em out, during which time you are tunnel-visioned like with a Sniper's scope. Once charged, you can activate a brief, concentrated sentry barrage at the spot you're looking at. Can't target it on a spot that the sentry can't actually hit, but you can aim it outside the sentry's range. Particularly effective with artillery, which will otherwise fire more-or-less randomly in a wide area. Can't target players; has to be locations. Since there are cases when you want it to shoot against a skybox, looking through the scope will probably show a laser leading from the sentry to the spot it'll aim at, to help.
Sentry replacement: Objective Helper. Can only be deployed in a capture zone or on top of a payload. Does small but constant damage to any enemy who is in the capture zone or near enough to the payload to disrupt it. Prevents enemies from capturing the point/grabbing the intel/pushing the cart/blocking the capture/capturing the intel/blocking the cart. May be impossible, given the varying custom payload models in use in some maps.
Grenade replacement (Demoman): Bombchus.