Will a 2-way coaxial splitter diminish internet speed with only 1 exiting cable?

Should be fine imo. Nothing pulling thru the 2nd port so I cant imaging it will make any difference.

Congrats on the stolen cable by the way.

2 way splitters usually lose 3.5db per leg no matter how many outputs are connected.

you also run into problems with cable internet if you dont have a 1000mhz splitter.

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The second exit port has nothing attached.

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You should put a termination cap AKA terminator on the unused port. But if you have to buy one, you ought to just get a coupler as already suggested. That would be a 1 dB loss vs 3.5 for the two-way splitter.

That open port the splitter could be allowing ingress in which would affect your speeds

The simple answer is yes.

Any splitter will cause the signal to be degraded. It doesn't matter if you only have one cable connected. If you only are running internet, and no cable from that line, you don't need anything special like adapters or amplifiers (At least with Cox Internet).

Now, the degraded signal may not even be noticeable because of the splitter. It really just depends on multiple factors such as bad splitter, distance to Cox Node, bad cable drop, etc.

Easiest way to test, is to run a speed test with everything setup as normal. If you're not getting close to what your supposed to, then either replace the splitter with a new one or get a coupler (extension adapter) Once you do this test your speed and you should see some increase.