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Certain languages have no third person pronouns and their speakers use nouns (such as "servant" in Japanese) to refer to other persons.
They explicitly state that they don't mind when confused humans refer to them as he/she/it/they.
This should not be a problem to your readers after some introductory explanation (in text or in a preface) and a few reminders every now and then during the narrative.
If you want to write in English without using words from another language, you could look at what translators do when they translate text into English from one of the existing genderless languages.
The reader will inevitably read how they speak and how they are referred to and create an image in their mind of the species that fits that portrayal, so ask yourself which pronouns best match the portrayal you are going for after asking yourself which kind of portrayal would be more appropriate to your story and why.
Craig has an important point hidden in his excellent answer: Gender is more than just sex organs.