Wellies wouldn't be my first choice for grip on a hard, smooth surface. They are too solid in the sole, and they invariably leave you with a lot of foot 'slippage' room inside, so that, as your weight shifts around, the boot is moving accordingly and not in a controlled way, as you walk. You want something a lot closer fitting round your foot, in softer rubber - trainers at the very least.
When I realised how woefully inadequate my current supply of footwear was I invested in some proper boat shoes - and they are fab. Expensive, but I feel rock solid in them. And I am no athlete.