Re-installing won't render the 3rd license used/obsolete. You have a license for 3PCs you will still be using it on only 2PCs as essentially you in wiping the current installation, then reinstalling on the SDD (total still 2PCs).
The avast license doesn't restrict you to X number of installs/re-installs, etc. but up to 3 unique (active) installations. What you can't do is have it installed on more than 3PCs at a time. So you can as mentioned use the resend license function to recover/be sent a copy of your original license.
Note that the 3rd license you have is counting down anyway as the license period starts at the point of purchase not the point of installation/registration.