Gillette.com offers its Gillette Men's SkinGuard Razor Sample for free with free shipping after you fill out this form. This newly launched men's razor is specifically designed for men with sensitive skin and razor bumps. You'd pay about $7 for one of these razors in your local drugstore.
Note that it's unclear how many samples are available.
Before you spend another dollar on items and services like these, check with your public library. You will likely be surprised by what it offers for free.