Send your resume to as many recruiters as you can. It is worth the postage. Generally, recruiters will not share your resume with any employer or give your name to anyone else without obtaining your specific permission to do so. The recruiter will call first, talk to you about a particular position and then ask your permission to share your resume with that employer. Your resume will be kept strictly confidential by the executive search firm.
Recruiters are professionals.
They recognize that in order to assist job seekers and professionals in their career development, they will need to ensure the professional of strict confidentiality. What this means is that the recruiter will hold all of your information confidential at all times. It is, in fact, safe to submit your resume to a search firm and not worry that the search firm will let it leak out that your are job searching. Recruiters will call you each and every time they wish to present you to an employer in order to gain your permission. Only after they have gained your permission will they submit your name or resume to the identified employer.