Use trimmer instead of razor and avoid the blood spots. 

I don't think so, do it a couple of days prior to the meeting day. 

I just want to say that it's good thinking. You're aware of the problem and you had the instinct that something isn't right. I concur with @robertroland, don't go with the irritated skin.

Yes, certain infections or diseases can be transmitted through skin-to-skin contact. it's best to let the skin heal fully and always use protection. Keeping things clean and using a proper shaving method or aftercare can also reduce irritation and risk.

It came to my mind because my skin is usually irritated after the shaving and is full of bloody spots. Those spots are not on my penis but in the surrounding area and it definitely will come in contact with her skin. Can diseases transmit that way?