(Indirectly) looking for a PhD before I have published a paper I am currently in the final (second) year of my masters degree (in bioinformatics) and am beginning to look around for a PhD. Admittedly, my resume so far is not very impressive: I did pretty well in courses but I do not have any published papers nor any conferences to speak of. 

A few days ago I had a conversation with a Cambridge professor who has visited my institution and has collaborations with many key researchers working on a topic I'm interested in pursuing (he himself does not work directly on this topic, to my understanding). 

The professor said that if I send him my CV he may be able to forward it to his collaborators.  

When I talked to my thesis advisers (I have two) about this, both of them told me that I would be far better off if I had a published paper, or at least a submitted one, before I apply for a PhD. Our intention is to try to publish the project I'm currently working on, but it is likely to be a few months until we will a manuscript that we can submit.

On the one hand, I agree with my advisers that a paper would improve my odds with respect to admission to a PhD program (in terms of finding advisers, scholarships, etc.) . On the other hand, I think that I am presented here with an opportunity that I might not have again as the Cambridge professor will probably soon forget me if I don't write him soon. 

So, I basically have two questions:


Is it a good idea to try to submit my CV at this stage? Could this have any negative effects or do I have nothing to lose?
If I do write to the Cambridge professor, what exactly should I include? If I write directly to a potential advisor I would of course enclose a cover letter and letters of reference, or at least list referees in my CV, but in this case I don't know if this is appropriate and I'm not wild about the idea of pestering my advisers by requesting letters of reference for this after they already told me that they don't think it is a good idea.


Any comments will be appreciated. 

Note: this question is somewhat related to:
Apply for PhD before finishing my Master&#39;s degree

Applying for a PhD before or after finishing master&#39;s

but I thought that having a contact makes my situation sufficiently different in order to ask a new question.
It sounds like the visiting professor was speaking in rather vague terms, just being a nice guy offering to help you make a connection with people in your target researc area.  This is nice, and under normal circumstances you would follow up by sending a short email and with a short CV attached, since that's what he suggested; however, there is in principle nothing to prevent you from writing directly to the people the visitor had in mind.
But I think your question is more about how to apply for a PhD program, so let's look at that.
I suppose PhD applications are different in Europe than in the U.S.  In the U.S., I would say:

Today is February 19.  If you have just started your last semester of your master's program, and have no plans for next fall, then you'll have to get cracking with your PhD applications.  Meaning, drop everything and get them out the door ASAP, hoping to either barely make the submission deadline, or hoping your application will be considered after the deadline.
If you can continue on in your current department for another semester or year, then write down the application deadlines for the programs you're interested in, work backwards from that, and sit down and talk with your advisors about your timeline.  You may be able to find some programs that allow a January start date, but watch out, teaching assistantships are typically given to August start students.

I am sorry I don't know about procedures, timelines and customs for PhD admissions in Europe.  All I can suggest is that you start by carefully reading the admissions information published on the target university's website.
You could take a look at Academia SE questions related to the PhD admissions process in Europe, and ask a question targeted at that specifically.
Additional notes: in general it is best not to go against one's advisor's wishes; your question did make me wonder if your advisors are trying to keep you in your current department.