Osmium is the densest pure metal, but iridium has an almost identical density, i.e. 22.56 for Ir, vs. 22.59 for Os.
The difference is far too small to give you a different feeling when holding a piece of either osmium or iridium.
While osmium and iridium are the densest pure metals, there is a range of composition in the osmium-iridium alloys which has a slightly greater density than both pure osmium and pure iridium.
That happens because the atomic concentration of Os is a little higher than that of Ir while the atomic mass of Ir is a little higher than that of Os.
While increasing the proportion of Ir in an Os-Ir alloy from 0% to 100%, there is a range where the atomic concentration decreases slower than the average atomic mass increases, so the density of the alloy becomes greater than the density of pure osmium.
At higher Ir percentages, the increase in atomic volume overcomes the increase in atomic mass, so the density becomes a little lower than for pure Os.
Unlike pure osmium, an Os-Ir alloy would not be dangerous to handle. Pure osmium is slowly oxidized in air releasing the volatile and extremely dangerous osmium tetraoxide.
In nature, the normal occurrence of both Os and Ir is as nuggets made of Os-Ir alloy, usually also containing ruthenium and very small quantities of rhodium.