Your situation was same as mine two years ago. My initial subject choice was the same as well. I did the CIE and i can only speak from my own experience.
Firstly, i think you should check with your exam board whether you can take Chemistry as a private candidate. Back then when i registered for my exam at British Council, they refused to operate the chemistry exam because it involves lab section. At the result, i had to change my subject to Accounting 4 month before the exam which i strongly advise you avoid.
Secondly, a level is really intense. I had a full time job when i first took the exam, and i got BBC which was really bad but it is a true reflection of the efforts and time the i invested in. Then i decided to quit my job, spent a year just for revising, and i got A*AA the second time. So i think you should estimate your own ability and clarify your goal first. If you are a bright student or you just aim for BBB or ABB then i think it’s totally possible to do a level while having a job.
Other than that, i think it would be the right decision to study privately. You can push the speed up or slow down according to your own capacity which make the studies more effective.