If you genuinely feel competent to do then do it, if you don't have it signed off by a bco then that would only be an issue if you try to sell the property and it's upto you if your willing to accept the difficulty/loss in value.
From a safety point of view the first thing to sort out is an isolation switch so you can safely remove power to the consumer unit, the dno should do it for you for a fee, you'd not be the first person to pull your own cut out fuse and fit one yourself but you'd have to make the decision on the condition of your incoming supply and if it's safe to attempt to do so, if the cut out or supply cable fall apart while pulling a fuse you shouldn't be touching you'll be in a huge mess ranging from having to admit to the dno you were doing unauthorised work to potential death.
After your at a point of safely isolating the incoming supply carry on with the rewire, personally I'd get a multi function tester even if it's uncalibrated, it'll still perform all the main safety checks correctly you just won't be able to rely on it's results for disconnection times but you can work them out with a pen and paper the mft results are just to confirm your workings out, someone with calibrated kit can do that at a later date, the mft should still be reliable for ir testing and testing for shorts and connections, you can do them reasonably reliably with a normal multi meter.