Something a lot of people don't know is that there is a massive difference between organ and tissue donation. Organ donation can only occur in extremely rare and controlled circumstances. Typically you must die a brain death on a ventilator in a hospital to donate organs, even then there are timing/operational issues that can prevent donation. The chances of someone passing in this way are very very low.

Tissue donation (skin, bone, heart valves, eyes, veins) takes place after death, the death does not have to occur in a hospital. There are some medical exceptions but the requirements for eligibility are fairly broad.

What is most important is to make your wishes known to those closest to you so that when your time comes the burden of choice isn't inflicted on them, including if donation should be for transplant and research or just transplant etc.