Recently I started running js mods, therefore I added the needed adjustments to the batch file. Additionally I implemented the findPath variable, @Isildur has been suggesting in the OP. Maybe someone can use parts of this for their own version, so I thought I'd share too.
#!/bin/bash
# Quit Vivaldi
osascript -e 'quit app "Vivaldi.app"'
# Find path to Framework folder of current version and save it as variable
findPath="`find /Applications/Vivaldi.app -name Vivaldi\ Framework.framework`"
# Copy custom.css and custom.js files to Vivaldi.app
cp /PATH_TO_FILE/custom.css "$findPath"/Resources/vivaldi/style/
cp /PATH_TO_FILE/custom.js "$findPath"/Resources/vivaldi/
# Save path to browser.html as variable
browserHtml="$findPath"/Resources/vivaldi/browser.html
# Insert references, if not present, and save to temporary file
sed 's| </head>| <link rel="stylesheet" href="style/custom.css" /></head>|;s| </body>| <script src="custom.js"></script></body>|' "$browserHtml" > "$browserHtml".temp
# Backup original file
cp "$browserHtml" "$browserHtml".bak
# Overwrite
mv "$browserHtml".temp "$browserHtml"
# Pause script
read -rsp $'Press [Enter] to restart Vivaldi...\n'
# Open custom.css in text editor
open -a "TextWrangler" "$findPath"/Resources/vivaldi/style/custom.css
# Open Vivaldi
open /Applications/Vivaldi.app --args --debug-packed-apps --silent-debugger-extension-api
