It is very unusual that a solicitor would advise you to change an arrangement that is already established and working. It isn't a solicitor's role to tell you what's right for your daughter - it's their job to advise you on legalities, and represent you to secure the outcome that you are seeking. So, I do wonder what prompted the decision to reduce his overnight contact - particularly since you were speaking to the solicitor about divorce (presumably financial) issues rather than child arrangements. I will ask - is this definitely nothing to do with maintenance?
You say that it is disruptive to your daughter for him to collect her on the Friday, but it isn't clear what you really mean by this. A court is going to be balancing the different needs and perspectives here to determine what is best for your daughter. How long is the journey to his home once he has collected her? What is the impact of a 7pm collection? Could that collection be done any earlier, or are there other ways to address the issues you're worried about without undermining your daughter's relationship with her dad by reducing their time together?
It is worth putting yourself in his shoes (and - crucially - those of your daughter) for a moment. You are trying to take away one of their nights together, as well as his chance to get her up, have breakfast, take her swimming etc on the Saturday morning. That's a pretty big deal, that reduces their quality time together. Doing so would need a pretty compelling reason. So, before this gets dragged through a court, I would encourage you to reflect on why you are doing this, and whether the disruption you are concerned about definitely outweighs the benefit to your daughter of this quality time with her father.
If you believe that it does, and you're doing this for the right reasons, then yes - it will probably have to go to mediation first (but see below for factors that may persuade a judge to take a different view).
If it does, then at mediation, you will both be expected to constructively look for compromises. For him, that would mean finding ways (such as an earlier collection) to address the disruption that you're worried about. For you, it will mean trying to find solutions that maintain the established relationship between father and child.
If either of you is unwilling to do that, it will move very quickly to court - particularly as you have arbitrarily imposed a change without consultation.
The court probably won't look favourably on your doing that - both parents are equal in the eyes of the law, and constructive co-parenting is about working together when you have worries about how things are affecting your child, rather than one parent assuming they can arbitrarily reduce the time that the child has with the other parent. That's not constructive, and it's not co-parenting. Neither parent 'out-ranks' the other. To be perfectly honest, if I were in your ex's shoes, then I'd be pushing for a hearing as rapidly as possible too.
All of which is a very long-winded way of suggesting that you need to try and figure this out by talking with the dad - not by imposing what you want. If you can't or won't do that, then he is within his rights to push for an urgent hearing. It will then be for a judge to decide whether to grant that on the basis that you are unlikely to engage constructively with mediation and the action you have taken is already impacting the child's relationship with a parent, or to insist that you go through mediation first. Either way, if this ends up before a judge either before or after mediation, you will need a compelling argument as to why the disruption to your daughter is so pronounced as to merit reducing the time that she spends with her dad.