Hey,
Yes theres away with no tools to find or track a Yahoo user.
First I do as told previously, contact Yahoo! with the user ID and the reason your contacting them.
As for obtaining there IP, you can try sending something to the other user through the messanger. An while he/she is downloading open MS-DOS or COMMAND PROMPT . An type in 'netstat -a' without the quotes. You should see the IP of the user while they are downloading from you.
*If your scared you wont know which IP is there. Then before you send the item to them type in netstat -a and take a glance of the IPs you have open. Then you will know which one is theirs when you send the item.

Now after you get the IP you can trace it by typing in MS-DOS or COMMAND PROMPT you can type 'tracert <IP HERE>' with out the quotes.
You can find out which is his ISP from the IP before his.(GENERALLY, not always) Once you find his ISP write it down, and do a whois on it. Then contact the Internet Service Provider(ISP). They will not give you the information of the user, however if you would like to press charges then you may contact the police and they can further the investigation.
Hope this is what you were looking for.