I am a hardworking person, who is always using the latest techniques and technologies as well as I can.
You can use 'I'.
As for he or she - that depends on whether the writer is male or female. There is no need to be gender-neutral when you know the sex of the person.
EDIT
In response to a comment I'll add the following. I assumed that the person referred to at the end of the sentence was the writer of the sentence. That doesn't have to be true, e.g.
I, John, I am a hardworking person, who is always using the latest techniques and technologies as well as Mary can.
In that case, if we didn't know the name/gender of the second person, the problem returns. However it is unusual to have a situation in which you compare yourself to an individual whose name/gender you don't know. In fact if you had a particular person in mind and weren't sure of their gender, it would probably be insulting to say 'he or she'.