Don't worry about disturbing people. It is the job of HR [the rats that they can be] to be disturbed by people and have the hard questions thrown at them. You phone the companies, ask to speak to HR regarding vacation work and then you pose your scenario. Make it very clear what you want to achieve and that you are asking for no remuneration in return for the exposure. If they ask you to send your CV through, make the CV professional. Use proper grammar. Try and keep the CV succinct, 1 page preferably, 2 pages at the absolute most. I prefer to include a covering letter with my CV (usually a separate document) detailing who you I am, what I wish to achieve at that company and why I wish to work for that company. Research the company when doing your covering letter, it shows that you have an interest in the company as opposed to just fishing for a job.
In the event that you land an interview, remain calm - interviews are not as scary as people make it out to be, they're usually pretty chill. Most interviews are panel interviews and you will be asked questions by the entire panel. The panel usually comprises 1 HR rep, the manager of the Business unit you will be slotted into and a senior (in your case) developer. When one of them asks you a question, look them dead in the eye when they're asking the question, address the answer to all. Do not be afraid to interject between questions with questions of your own, it shows that you're not timid. At the end you will be allowed to ask your own questions, be thorough and engaging.