Changing path of data & log files on the fly

We have a SQL Server setup as a publisher to 15 subscribers. We need to change the path of the data & log files to a new drive (added a new harddisk). We plan to take a cold backup of the database and shift the data & log files to the new drive. Then we just attach the data & log files from the new path.

Will this disturb my existing replication Setup?
Is the the correct procedure for changing the path of the existing data & log files?
What is the appropriate method for shifting data & log file of a live database to a different location (directory/drive) ?

thanks in advancedisable replication;
sp_detach_db;
move files to new location;
sp_attach_db;
enable replication.|||Thanks for the suggestion. I'll try this out and confirm back. Thanks again anyways.