The answer is - as always - it depends :)
In general, you can truncate (not delete!) the table core_url_rewrite. If it is empty, your SEO URLs like brilliant-whisper-300-1483.html will not work for the time being. But if you do a full reindex of the catalog URL rewrites, these URLs will be generated again, so that your SEO URLs should work again.
If you struggle with a very big core_url_rewrite table, then have a look at this Magento StackExchange question.
What can cause problems is if you did one of the following:
- You changed the URL key of a catalog/product and ticked the box
Create Permanent Redirect for old URL. Assumed you changed the URL key from my-old-product-name to my-new-product-name. Then, when this box is ticked, a rewrite from my-old-product-name.html to my-new-product-name.html will be created in the core_url_rewrite table. If you truncate the table, this rewrite will be gone, so that your old product URL will not work any more.
- You created custom URL rewrites under
Catalog - URL Rewrite Management. These custom URL rewrites will also be gone if you truncate core_url_rewrite.