Not big enough in what way? A normal probe should be able to handle the distancing and the small current fine. Maybe it would lack insulation but I wouldn't use the word "big" for level of insulation.
Typical probes are rated for 600 volts (CAT III), so you'd have insulation rated for 600 volts between your fingers and 30,000 volts, which is kind of hazardous.
When you combine a running transformer and weak insulation, and also there's no exposed metal where you intend for the current to go. So that probably comes off pretty differently.
But my use of the word "maybe" is more because of overall confusion about the word "big".
Here's a recent Twitter video showing what happens when you combine a flyback transformer and faulty insulation: https://twitter.com/zh1nu/status/1673487720780529664