Catrin, you will find that as you get stronger, the weaving thing will occur at much lower speeds, or even go away. I can easily climb at 5.5 for a very long time, and that's just what I did in Spain (well, I estimate this, since I had no computer). I have seen my computer at 3.5 at certain points on really steep climbs, but that would be just for a little bit, to rest.
I do think its safer to walk, though, if you think cars are around and you are weaving. A couple of weeks ago I was coming home from a ride with a friend. We were in her neighborhood, just chatting and going very slowly. A younger woman ('20s?) passed us on the left, on an older bike with a standard double, at the beginning of a little hill. She looked a little proud of herself for passing us old ladies, and then I noticed she was completely on the wrong side of the road, weaving horrifically. I told my friend (a newer rider) to watch, and I accelerated up the hill, spinning, and passed the younger person. She was totally red in the face and stopped in the middle of the road. She either didn't know how to shift, or she should have walked.