If you share those websites tabs to email you can launch email after clearing your chrome data and relaunch those websites. You won't lose them.
Notice chrome has three vertical dots on the top right corner of the browser.. Click it. Scroll down until you see share. You have many choices of where to share your chrome tabs. You can share to any or many of the choices.
First, click on the first tab you want to save. Then select the vertical dots. Scroll down until you see share. Click email or note pad, whatever retrieval system works best for you. Select it. The program launches either with the saved URL or information if you've actually selected specific information. I like to use email because I can find the information on all platforms (phone, computer, tablet). Send yourself an e-mail..
Repeat steps for each tab you want to save.
When you are done clearing chrome data, log into your email. Select your emailed tab email. Open it and launch. Save your tabs.