If it’s any consolation, it’s better to neuter and vaccinate on separate occasions. Vaccines work by challenging the immune-system so it starts to produce antibodies. When an animal (or a person) just have been operated on, the immune-system is occupied with healing the surgical wounds. That may mean that the body won’t be able to make enough antibodies – or that the animal (or person) can’t cope with both these challenges and thus get very ill.
There is always a slight risk with any vaccine so the animal (or person) who gets them should be in as good health as possible when they are vaccinated.
My vet don’t examine the bunny before giving the vaccines (myxi and calici), but of course they ask if the bunny is healthy. With an examination it would be seriously unaffordable and people wouldn’t vaccinate their bunnies. If you feel confident that your bunny is well you could perhaps call several vets and ask them what their routines are like and their prices.