It is not completely safe to run LiveUSB, just like it is not completely safe to run a dedicated computer. The manufacturer may have introduced a vulnerability into either the computer or USB drive at the hardware level. There are steps to take that will allow you to safely use with a LiveUSB or dedicated computer, assuming that the devices are not compromised on a hardware level.
This addresses the LiveUSB security issue. If you use a USB device with an integrated switch to disable write access you can be sure that the contents of the drive don't change. This is assuming the device never leaves your sight (since someone can just flip the switch and modify files on the drive) and assuming that you trust the drive manufacturer to correctly implement the write protect feature.
I would be careful where I got the USB device from. They have microcontrollers in them, which can be reprogrammed.
Of course, if you want persistence (wallet files, etc.) you need to disable the write protect or have one flash drive for the OS and another for the data.
Ultimately it is up to you to answer: Do you have enough bitcoin to justify (a) dedicated computer(s)? I personally feel a LiveCD is sufficient, with a flash drive for the (encrypted) wallet.dat.