I am somewhat sceptical about his claim.

Convinced means having a strong belief in something. It is the opposite of unconvinced. Someone who is convinced is certain that something is true or that something will happen.

Credulous means easily persuaded or believing too easily. It is the opposite of skeptical. Someone who is credulous is likely to believe anything they are told.

Hopeful means having a feeling of expectation and desire for a certain thing to happen. It is the opposite of hopeless. Someone who is hopeful believes that something good will happen, even if there is no guarantee.

In the given sentence, the speaker is expressing doubt about the claim. This suggests that the speaker is not convinced or certain that the claim is true. The speaker is also not easily persuaded or believing too easily. Therefore, the speaker is not credulous. The speaker is hoping that the claim is true, but they are not certain. Therefore, the speaker is optimistic.