I've done 3 seasons of riding Meadowbank but I've never been to Glasgow. Meadowbank is basically fixed gear & no brakes. Glasgow have a list of whats needed if you're bringing a bike as per below, from HERE
PS no mention of fork requirements so I think you'll be OK.
WHAT IS THE SPECIFICATION OF A SIR CHRIS HOY VELODROME BIKE?
If you are bringing your own bike to the velodrome it has to be a bike intended for track use. Please ensure that:
the frame does not have any braze on additions
track drop outs are fitted
it has tyres that are intended for track use
new tyres have been properly prepared
bar ends are fitted and secure in handlebars
there are no quick release spindles
wheel spindles do not extend beyond the track nuts, front and rear, and are sawn off flush with the nut and filed smooth