I wouldn't. The main problem isn't with the compatibility, etc. In fact, most of the wallets do actually offer a portable version. The main issue is with the security.
If you're going to bring the portable wallet around, you could very well be losing it if you forget to bring it along after using it on the computer. Public computers aren't exactly safe at all, using your wallet on it could very well have it being compromised. If you need portability, consider getting a mobile wallet on your phone; doesn't address the first point but it addresses the second.
A portable hard drive is relatively heavy and unreliable at times. It's not rational to be bringing around a bulky metallic case when your main function is to have a portable wallet. Hard drive (not SSDs) are very prone to failure if you drop them.