If you're not currently running replication, you probably won't have any problems moving the distribution database files.
If you were actively running replication, I'd try this:
-- 1. Stop the Log Reader and Distribution agent jobs on the Distributor.
-- 2. Take distribution database offline.
ALTER DATABASE distribution SET OFFLINE
-- 3. Move distmdl.mdf and distmdl.ldf files to new location (cut/paste).
-- 4. Modify the database to use the new file location.
ALTER DATABASE distribution MODIFY FILE (NAME = distmdl,
FILENAME = 'K:\MSSQL.2\MSSQL\Data\distmdl.mdf')
ALTER DATABASE distribution MODIFY FILE (NAME = distmdl_log,
FILENAME = 'K:\MSSQL.2\MSSQL\Data\distmdl_log.ldf')
-- 5. Bring the distribution database back online.
ALTER DATABASE distribution SET ONLINE
-- 6. Restart the Log Reader and Distribution agent jobs for the Distributor.
Note: I haven't actually done this for the distribution db, but I've used a similiar process to move subscriber dbs to a new drive.