How do I reindex a MYSQL table using a different disk?
There is the Percona Tool called pt-online-schema-change
If you can tolerate downtime, you can try the following:
Suppose you have the following

datadir is /var/lib/mysql
MyISAM table named mydb.mytable
You have large disk volume mounted on /backup

You could do the following
mysql -u... -p... -e&quot;CREATE TABLE mydb.mynewtable LIKE mydb.mytable&quot;
mysql -u... -p... -e&quot;ALTER TABLE mydb.mynewtable ADD INDEX (acctnum)&quot;
#
# Create Symlinks Pointing to Another Disk
#
cp /var/lib/mysql/mydb/mynewtable.MY[ID] /backup/.
rm -f /var/lib/mysql/mydb/mynewtable.MY[ID]
chown mysql:mysql /backup/mynewtable.*
ln -s /backup/mynewtable.MYD /var/lib/mysql/mydb/mynewtable.MYD
ln -s /backup/mynewtable.MYI /var/lib/mysql/mydb/mynewtable.MYI
mysql -u... -p... -e&quot;INSERT INTO mydb.mynewtable SELECT * FROM mydb.mytable&quot;
mysql -u... -p... -e&quot;ALTER TABLE mydb.mytable RENAME mydb.myoldtable&quot;
#
# Erase Symlinks
#
rm -f /var/lib/mysql/mydb/mynewtable.MY[ID]
#
# Move Newly Made Table Back
#
mv /backups/*.MY[ID] /var/lib/mysql/mydb/.
mysql -u... -p... -e&quot;FLUSH TABLES&quot;

Seems like a lot of work, eh ??? Try the pt-online-schema-change first.
UPDATE 2012-08-22 11:56 EDT
I am not sure what would happen, but please hear me out on this suggestion: Try executing a repair on an empty .MYI file.
How do you do that? Take my idea from my first suggestion and augment to swap the new and old .MYI.
mysql -u... -p... -e&quot;CREATE TABLE mydb.mynewtable LIKE mydb.mytable&quot;
mysql -u... -p... -e&quot;ALTER TABLE mydb.mynewtable ADD INDEX (acctnum)&quot;
cp /var/lib/mysql/mydb/mytable.MYI /backup/.
rm -f /var/lib/mysql/mydb/mytable.MYI
cp /var/lib/mysql/mydb/mynewtable.MYI /var/lib/mysql/mydb/mytable.MYI
mysql -u... -p... -e&quot;REPAIR TABLE mydb.mytable&quot;

This should perform an in-place linear index rebuild.
Give it a Try !!!