If your claim dispute is rejected, the best course of action to still have your video publicly available on YouTube (and monetized, if applicable!) will be to replace the copyrighted tracks that are causing problems with alternatives.
You can look for replacement tunes on Fugue manually, or use a neat feature offered by Youtube. It allows you to choose tracks from YouTube's own extensive royalty-free library. Here's how to access the YouTube option:
Open YouTube Studio and select the Content tab from the menu.
2. Under Uploads, find the video with a copyright claim. Move the cursor over the "Copyright claim" text, and click on "See details" in the popup.
3. Click on "Select action", then on "Replace song".
4. You'll then be presented with a list of possible replacement tracks from YouTube's stock music library.