The dryer motor itself is 150W, so it’s drawing very little current. The comment about “no extension lead” will likely be there because the dryer includes a socket that you can plug an additional electrical device/devices into (eg. fan heater, electric fire!) potentially significantly raising the current drawn through any extension cable being used…
So long as you’re sensible, there shouldn’t be any issues using the fan with an extension cable. As always, use a quality cable and ensure that all the things you’ve plugged into it don’t in total exceed the extension’s rating: