I haven’t tried this, but it should work:
- close Chrome
- move ~/Library/Caches/Google/Chrome to your external drive
- right-click on the folder and choose Create alias
- rename the alias to Chrome and move it in ~/Library/Caches/Google/
Explain how Chrome is “killing” your SSD? The cache is a repository of visited web page assets. I highly doubt Chrome can write enough files to its cache to “kill” a SSD.