Can I Submit a Professor's Recommendation Letter from my Personal E-mail?
This seems like a bad idea and I would do it only as a last resort.  Even with the disclaimers, it could raise questions in the reader's mind as to whether you forged the letter.  I think it was not appropriate for the professor to ask you to submit it yourself.

If the letter writer isn't able to submit the letter himself, a common alternative is for some other university employee, such as an administrative assistant, to submit the letter.  I would suggest pushing for something like this.