Re: What would be a proffesional way..
I think the term “provide me training” won’t work. Employers are usually interested in “what YOU can offer to them”.
Also, employers kinda feel insecure when there are no legal sign-ups, and thus allowing an outsider to work is no good. Other alternative term used is volunteer work, which may become bit easier in case if u have any contacts/references in that company. Usually not-for-profit organizations allow for volunteer work; i’m not very sure about businesses.
If you’d give more details like your field, type of ur target company etc., may be someone could give you better suggestions.