Is there a way for the all subscribers list to not get updated?
No. All Subscribers acts as the master list of all subscriber data, and a subscriber must be on the All Subscribers list in order for that sub to receive email. If a particular SubscriberKey has more than one email address field in a DE, the All Subscribers EmailAddress value will be updated with whatever email address is selected for the particular send.
we only want to send to the alternate email address once.
This is quite simple - just send to the same subscriber again, but make sure to designate the primary email address as the email address you're sending to. Yes, this will update the All Subs email address again with the primary email address, but it will accomplish what you're trying to do: send to alternate email once, and then continue sending to the primary email.
A way around this could be to create a new subscriber for the alternate email address. For example, you could have SubscriberKey_PrimaryEmail and SubscriberKey_AlternateEmail. This unfortunately introduces a potential data management issue, having to account for 2 subscribers for 1 real-life identity. But from a system perspective, it could allow you to bypass the All Subs update.