You don't have to charge with 1A or whatever. I also doubt the 'constant-current' phase of the charge cycle really has to be constant. The point, as I see it, is to charge the cell with a current source (whatever it may be) until it reaches its float voltage at which point any further increase in voltage might – and eventually will – damage the cell. I can't see why there would be an inherent lower limit on the charge current.