I was there in the morning on Sept 30th last year and saw people walking up to buy tickets. The line at that time of day was at most 2 or 3 people, though they might have had to wait for the start of the next available English tour.
The online ticketing system (https://www.wieliczka-saltmine.com/) shows how many tickets are available for each time slot on each day. So you could check occasionally and decide later if you should purchase your ticket ahead to ensure availability.
Looking at dates in September, 10am appears to be a very popular time: fewer tickets available then. So you might keep that in mind in timing your own arrival either before or after the 10am tour slot. There are English tours every half hour.
At the bottom of the page on which you select your tour time, it also says "Remember, tickets are available at box offices on site during opening hours." That sounds as though some tickets are held back to be made available to people who just show up to buy a ticket.