I don't trust rubber band mounts after a few months so I reinforce mine with removable putty, like Blu-Tack, Loctite or Scotch brand blue or white removable putty. Works great. I've used the stuff for years to attach video camera mounts to my helmets, without using the more permanent 3M double stick tape often included with mounts for cameras and other electronics.

On my most-ridden bikes, I use Blu-Tack putty to hold a USB battery on the top of the frame near the seat post to simultaneously charge and run my rear-facing video camera, which has a three year old battery that won't hold a charge more than about 30 minutes. With the USB battery and cable it'll run for hours. So it's pretty secure stuff.

For now I'm using a combination of Blu-Tack gum and rubber mounts to secure my XOSS bike computer to the top of the frame behind the headset (the stem and handlebar are already full up, between two headlights and a front-facing camera). But I'll probably get one of those computer mounts that attaches to the headset cap or stem clamp for the handlebar. Looks cleaner, easier to see.

As Bald Paul noted, you can use fingernail clippers to nip old zip ties without scratching the bike. I've also used zip ties for years to arrange the criss-cross cables on my bikes with bar-end shifters and old school brifters. I have a pointy jaw pliers style toenail clipper that's never been any good for toenails but works great to snip zip ties and similar items, so it stays in the tool box.