LDPlayer has a lesser-known "green" version. You can download the LDPlayer installer, extract it using 7-Zip, and run the ldplayer.exe directly. It will still create folders in AppData , but you can force it to use relative paths.
No official version exists. Any website claiming to have "BlueStacks Portable USB" is almost certainly distributing malware. Bluestacks Portable No Install
Below is a detailed breakdown of what this version entails, how it works, its potential benefits, and the associated risks. LDPlayer has a lesser-known "green" version