"What gifts should I not give to Chinese people?"
Omitting 我 is not entirely an implication of the subject but it makes this a common truth. We can do it similarly in English by saying "What gifts should not be given to Chinese people?" (Note: It is rarely expressed in Chinese in passive voice for such case, such as 什么礼物不能被送给中国人？which is grammatically correct but not acceptable in actual application.)
Yet the word order of your sentence is not correct. It should be (有)什么礼物(我)不能送给中国人？