How can I reinitialize some MyISAM tables without restarting MySQL?
Absolutely !!!
Suppose you are moving a MyISAM table with the following characteristics:

MyISAM table is called mydb.mytable
datadir is /var/lib/mysql
Moving From ServerA to ServerB

You can move it to another folder without disturbing any other DB activity
Here is how
Step01) Create the Target Database on ServerB with this command
CREATE DATABASE mydb;

Step02) Copy the table to the mydb database on ServerB
Run this rsync on ServerA
rsync -av --progress /var/lib/mysql/mydb/mytable.* ServerB:/var/lib/mysql/mydb

That's it. The table should be immediate registered in the information_schema without a restart. To verify that the rsync worked, login to mysql on ServerB and run this:
SELECT COUNT(1) TableExists FROM information_schema.tables
WHERE table_schema='mydb' AND table_name='mytable';
SELECT table_rows TableCount1 FROM information_schema.tables
WHERE table_schema='mydb' AND table_name='mytable';
SELECT COUNT(1) TableCount2 FROM mydb.mytable;

If TableExists is 1 and  TableCount1 =  TableCount2, CONGRATULATIONS !!!
If you want to double check the rsync, run thi command on both ServerA and ServerB
CHECKSUM TABLE mydb.mytable;

Both checksum values should be identical
Give it a Try !!!