The safest method? Install from your original Brood War CD (patch it to 1.1.6.1 using the official Blizzard patch archive), then copy the entire folder to a USB drive. That creates your own legitimate portable version.
While Blizzard Entertainment continued to patch the game for years, version 1.16 (and its sub-iterations like 1.16.1) is often viewed by the hardcore community as the last "pure" version of the original game before the massive changes brought by StarCraft: Remastered . StarCraft- Brood War 1.1.6.1 Direct Play Portable