Is it ok if I use right away the disavow tools without asking the webmasters?
You can submit a disavow request right away, and to be honest, from what google has made public about the disavow tool, it is probably BEST to do it first, since it can take a LONG TIME for the disavow tool to work - like, months or a year... or more!
In the meantime, do the bad links point to important pages that you CAN'T change the URL / file name of the page (like your home page).
Or do they point to internal pages where it would not be a problem to change the URL (by changing the file name) to something else?
Because you could rename some of the target pages to different names so those bad links would be pointing to a 404 page.
After that, I would start contacting webmasters seeing if I could get the links removed.
If you still have any old link exchange programs, get rid of them ASAP.
Hope this helps.
I have no idea if there is a way to cancel a reconsideration request but that is the last thing I would worry about.