How to run current mails from MacBook and access or search old mails from an external hard drive?
You can try the following approach.

First of all, show hidden files on your Mac by typing, on Terminal, the following command (substitute 'NO' to 'YES' if you want to re-hide files).:

defaults write com.apple.finder AppleShowAllFiles YES


Relaunch the Finder. Now, go to youraccount/Library/Mail, then enter the folder Vx, where x is a number corresponding to your Mail version.
Then, if you have an IMAP account (i.e., Gmail), enter the imap folder. 



Accessing  all the listed folders, you can see all your emails, with extension .emlx. If you double-click on it, it will be opened a Mail windows, where you can read the email and perform any operation you want.



You can just copy the mails you are interested in a new folder, in your external drive, and open from there when you want, for example, to read or reply to one of them.