URL: https://desktop.telegram.org
They already have a portable version (https://telegram.org/dl/desktop/win_portable extract the .zip and run the .exe. doesn't write anything in registry) and it auto updates but I'd somehow prefer to have a PortableApps version.
Telegram is OpenSource, source available at https://github.com/telegramdesktop/tdesktop.
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You'll be happy to know that it was added to our app lineup in May
https://portableapps.com/apps/internet/telegram-desktop-portable
Sometimes, the impossible can become possible, if you're awesome!
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