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No worries!
For what it's worth I used to ride 15-20 mins to Herne Hill on track gearing, usually around 86gi since I never was fast enough to need 90+ :( . It takes 2-3 mins to fit / remove a front brake once you've done it a few times. And even if you go brklss don't ride like you're on a track bike, ride like you're on a pashley and you'll be fine. Leave a bit earlier, take everything easier, nbd. I would suggest a brake getting to and from the velodrome and then yeah give the rubber a wipe down and you'll be grand
If you are looking for a 52cm I am still selling this. Is good bike, is fast bike. We can talk price if you're interested https://www.lfgss.com/conversations/322472/