To me, I would say that the Career Objective should be included in the CV, as I believe it to be what you have done in your previous jobs and therefore shows the relevant skills you have in more details.
As for the cover letter, I would say to indicate you have experience in the areas, but dont list everything and direct them towards the CV
Career objectives are usually very brief and start with “To…”, e.g “To bring…” or “To work…”.
In short, it states what you plan to do and what your “objective” actually is.
Your cover letter should not just reiterate what you’ve already written in the CV. Of course, several things may be similar, but you don’t want to be giving the employer two pieces of paper with the same things written in two different ways.