Impact of moving the ldf and mdf files temporarily for few hours
You should don't have any issues I have done this many times before with no big issues.

One thing to consider is that if you have binaries in  E drive, you may have some issues, otherwise should be ok to go. 

From what I remember in the past you should check OS privileges, once  I had issues with the SQL Server account access to the drives. 

Another tip: If you plan to go with the move of the datafiles, you may want to try to shrink the tlog files before put offline, this way you will save some MB/GB and copy time will be faster.