Is it possible to install an application on a jailbroken phone without cydia or installer? I have tried both cydia and installer in the past and have always found they slow down my phone.
The only way Cydia should be slowing down your phone is after you install a bunch of crap. I've found that if I keep it simple it runs as though it isn't even JB'n.
Yes, it's possible. Cydia is simply a graphical front-end for apt-get. You'll need to locate the source and the package name and then you can install it from command line if you have SSH running on your phone.
I wouldn't touch Installer with a 10 foot pole. On the other hand, if you think Cydia is too bloated, then IMO there really is no reason for you to have jailbroken your phone.
Cydia was the only reason I felt the need to Jailbreak. Sure back in the 1.1.x days I used Installer, but the new Installer is just horrible, they should have kept the old UI, it's way to bloated for me, Cydia is the way to go.
EDIT: The guy who made Cydia made cycorder...So Cycorder might be to bloated for you aswell.