I’d give it a go if I were you. The capacitor blew on our tumble drier last year and I decided to try and fix it. Admittedly a tumble drier is probably a lot less complicated than a washing machine but it wasn’t as hard as I was expecting it to be.
It took a few attempts as I had to dismantle the entire thing (drum out etc) to get to the capacitor and kept running out of time – I had to put it back together after each aborted attempt due to lack of space and two toddlers in the house.
When I finally gave myself enough time I stripped it down, got the capacitor out, popped down the local hardware store for a new one (£16), put it in and put the thing back together. It probably took me a few hours but I felt much better for it, it saved me the cost of a new one, and I could happily do it again in under an hour I reckon.
Edit: As above, if you do have a go, take lots and lots of photos.