Just pretend that you're ill and get a day off. Loads of people do/did this at my school every year. My last Sports Day was in Year 8 and I never got called out for it. If you're lucky, your teachers won't even care; they know it's loathed by anyone not remotely sporty.
Do you have to participate? At my sports day we all had to sign up for races so we did but then when we were called out to do the race we just went off to another side of the park so they couldn't find us or just told the teachers we weren't going to do it and there was nothing they could do about it... and there wasn't because they either were so busy they didn't even care or they didn't care because they were getting the day off teaching and just wanted to be relaxed.
Or you could be 'ill'. I'm sure you won't be the only one absent and they might not even call home because they'll be busy.
do what I did on my last (compulosory) sports day, put your name down for something easy (400m relay for example) then wait as rugby-bums (what we called them) who want to show how awesome they are steal it off you....lol