I really wouldn't recommend this, since you could end up gunking up your MicroUSB port and causing your phone to no longer make a good connection via USB. That's much harder to repair. If it comes down to this, spend the $3 on a new MicroUSB cable before you start sticking tape into your phone's USB port.
As far as repairing the cable itself, it can be tricky. The little prongs you're talking about look like hooks but they are actually solid "wedges." Your best bet is to try getting behind them by going in through the "top" (the end of the slit the prongs are in that is closest to the phone end) with a very thin needle.
Honestly though, I would just spend the $3 and buy a new cable from Monoprice.
Premium USB to Micro USB Charge & Sync Cable 6ft- Black - Monoprice.com
The "premium" cables are worth the extra cost. The only problem I've ever had with a USB cable is what you're describing (the prongs giving way and the cable not staying in the phone). That usually happens to me after about a year. I've had the premium cable for two years and it is still going strong. Either way, they have a lifetime guarantee and will replace the cable (including for this issue) without charging shipping.