How to display professionalism when cold emailing a private seller that you want to work with? (most sellers only display their email address)

Great question! My response is based on experience...
There's companies you must assume their limited contact info is for a reason.
There's companies like startups, local or midsize firms that are more welcomed even if they lacked the knowledge of value in more contact info in their sites.. What i have done in the past is Google a relevant employee and try a variation of their name and email.. Sometimes it works sometimes it doesn't.
If you can't get a name then to that general inbox address yourself with as a higher rank title as possible without lying or becoming liable, state that you are requesting a contact number or address so that you can stop by and introduce yourself and maybe drop off some goodies (I have dropped off sweets, donuts, & coffee) aks that if they prefer to give you a call and schedule a visit to please do so by a certain date.

This approach very often works for me.

Never, even in person, do you introduce yourself for the purpose of gaining something from others and immediately ask for a favor or their business. Build a relationship even if is a thin one... Then when you know your offering is either welcomed or needed do you pitch or ask...
This might limited the amount of pitches you do online but the quality will increase. :)

Adding to Humberto's message, I would add that you MUST customize your message.

Write a clear letter/email and in it, explain very clearly what you can offer to the firm to improve them and why they should meet you.

The message can be short but must be very precise. Use all Humberto's techniques to follow up and get a second message to the prospect and aim to have a conversation / phone call / meeting.

Make yourself memorable - first in print and secondly in person and you will stand a good chance.

You may want to download this ebook I wrote about writing cold emails.
http://creativeagencysecrets.com/downloads/cold-emails-introduction-training-expert-advice/

Rebecca

The best way to show professionalism and respect is not to waste the listener's time. Let them know you're good by providing an example of your service for them. This takes your experience and references out of the equation, and eliminates the risk of them giving you a shot. It also differentiates you from 99% of your competitors who are too lazy to do this.

For example, if I were a copyrighter, I might write:

"Bob, I'm a professional copyrighter specializing in helping online artists get more sales for their art. I've rewritten listing #17 for you in accordance with proven marketing principles to help you get a greater response. Try it out, and if it works for you, the only compensation I ask for is 2 referrals to other good artists you think would appreciate my service. And if you want additional listings rewritten, I'd be happy to redo them for $50 each."

Once you get your first few clients this way, you'll have to do less of this and can rely more heavily on your references.

Good luck!