We live not far from the river and a few years back our neighborhood had a rat infestation. We put traps and poison in the basement which got rid of the rats. Then we sealed up the basement by closing up the air vents in the foundation. The droppings are still in parts of the basement and have not been a problem. We're healthy.
I don't know why the droppings would be toxic. It's just poop. It dries up and emits no vapors. If you want you can go up to the attic and sweep them up if there are boards or a floor or if the insulation is covered with paper. I see no need to sanitize. I would wear a mask because the attic also contains lots of dust and pollen. I would guess that the dust and pollen which is moved around with the air to be more of a concern. Once the poop is dry it is heavy and will not circulate in the air.
Rats can do structural damage. And if they continue to have access their poop would build up over time and may mold I would look at air vents and be sure that they're screened. Easy to do yourself and wouldn't cost much at all.
If you do decide to change insulation, etc. I agree with Momwithcamera. I suggest that having a contractor do the job would be less expensive.