Getting to 100,000 feet is cheap. Accelerating to orbital velocity is expensive.
Before launch, the shuttle and boosters have a mass of 2030000kg. Lifting all that to 30500m requires 607GJ. (Slight over estimate because you would not need a full external tank if you start from 100,000 feet.)
Without the external tank and boosters, the shuttle has a mass of 109000kg. Magically accelerating only that to the velocity of the international space station (7680m/s) without any rocket fuel requires 3200GJ. In real life, over 90% of the initial thrust is used to accelerate rocket fuel. This percentage falls as the fuel is burned, but you need much more than 3200GJ when you include accelerating some of the the fuel to some of the final velocity.
You might save 5% on the cost of a space shuttle if you had a free ride to 100,000 feet. You are looking for a payload of about 200,000kg. Here is what is/was/might be available:
Payload: 160,000kg Currently incomplete and out of money.
Payload: 40,000kg. Zeplin/helicopter hybrid currently under development.
Payload: 83,000kg. Currently in pieces under the sea.
Payload: 72,000kg. Currently in pieces under the sea.
Payload: 10,000kg. Currently not functional. (LZ-130 scrapped after 129 went down in flames)
Payload: 2000kg. The biggest I could find that actually flies today.
I doubt that any of these could get close to 100,000 feet.