I'll only send emails that are relevant for the recipients. Indeed, I would expect that many of them would be happy to receive my emails. However, I'm not sure of the legal position.
Don't. There are legal restrictions on sending unsolicited emails and this type of activity will usually fall foul of them. Under English law - which broadly reflects the position across the EU - the Data Protection Act restricts the use of email addresses that constitute personal data (e.g. email@example.com) while the Privacy and Electronic Communications (EC Directive) Regulations restrict the use of email addresses that belong to "individual subscribers". There is a gap in the regime, but it may be impractical to check whether a particular email address falls through that gap, and it is almost always impractical to check a whole list.
Legal issues aside, almost no one wants to receive unsolicited emails, not matter what the offer. And if your offer really is that good, you should be able to use it to build a good opt-in based list.