D-32, I agree with the guys that said you should try to learn both pick and finger style. Coming from a guitar background, you might find picking, at least for now, easier. Those of us who use picks (I'm one) use heavy picks. However, you might want to start with a medium, and work your way up. The girth of a bass string takes a little more umph, than a guitar string. Finger playing is a new animal for you. Your fingertips aren't tough, yet, and your fingers aren't as strong as they're going to be. It's going to take time. So, for now, I would urge you to learn every song using both pick and finger.
Crossroads and the Lemon Song are pretty advanced technically. The main part of Crossroads is pretty easy to pick up, although it's a fast tempo. The improv/solo portion is a monster. This has been a project song for me, for quite some time. Lemon Song is also a very difficult song. While it's slow-medium blues, there is a lot going on in that song. If you really need these particular songs, on a one-month timeline, I'd urge you to get a bass teacher.
Unfortunately, most Cream and Zep songs are pretty advanced. If you're not dead set on those particular songs, you might try something like Sunshine of Your Love. It's medium tempo, amd pretty straight forward. For the outro, think galloping horses. You'll get it.
Instead of Lemon Song, you might consider Red House (preferably one of the live versions). It's a pretty basic blues in A major. Also, a couple of minor blues that come to mind are Key to the Highway (Am) and Blues at Sunrise (F#m). Both are slow blues. This would give your right hand a more mellow tempo to start out with.
As for the other comments, the first electric guitar was, indeed, Rickenbacker's "frying pan". It was an ugly lap steel guitar that looked like a frying pan with strings.
Guitars are not always played with picks, either. A couple of great fingers only guys, that come to mind, are Albert Collins and Mark Knoffler, although there may be hundreds more.
And the first electric bass was the Fender Precision. This bass came with a finger rest. Not a thumb rest. It was originally designed to be picked with the thumb, and not the fingers. Just a little fyi... don't want to start an argument.
Hope this helps. hrb