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Wouldn't that cause some kind of time paradox if Clark is taken from an alternate future of his own universe and stuck into the past, thereby erasing the future from which he was removed?
Yes. That was the point of this exercise. Clark's original timeline was replaced with whatever comes out of Clark moving into the past.

One thing I thought of was that since "Clark" was already present in this timeline, then baby Clark's ship would be forced into another timeline.

Another thought was something along the lines of this...

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As Clark stepped into the past, a ripple tore through spacetime. Since, as everyone knows, temporal shockwaves moved backwards through time, it reached the planet Krypton 63 years before the birth of Kal El. As the shockwave passed through Krypton it caused a subtle but critical shift in the fluid dynamics near the planet's core. As a result of this shift, a swirling eddy of molten iron deep in the core had it’s pattern disrupted and dissipated. This eddy had been destined to grow into the core instability that would have destroyed the planet Krypton. Sixty three years later Kal El was born to a healthy and stable home world.
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That doesn't really solve the paradox problem, but at lease we don't have the Oedipus issue to deal with.

As I said, you can get really crazy when you start messing with timelines.

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I'm not touching that one because of the paradoxical Oedipus issue with a Kryptonian soulmate bond connecting him to his mother after his father died. I'm getting a splitting headache just reading the scenario.
smile I'm not writing it. I just thought it was an interesting variant of that problem. evil

Bob