The best option you have is to buy some bolts, washers, and nuts to replace the pin. Bolting it down will allow you to tighten the heatsink tighter than the pin will. However, you shouldn't overtighten it, otherwise it could bend the brace on the heatsink or cause damage to your motherboard.
If the pin from your older heatsink is the same size and dimensions as your new pin, then yes you can use the old pin. However, if they are not the same dimensions, you can possibly use both/all the pins from your old heatsink to replace both/all the pins from your new one, as long as they are roughly the same length.
If neither of those works, then you might want to send an email to the manufacturer of the new heatsink, requesting a new replacement pin.