Ceiling light fixtures are about the simplest, safest electrical device there is.
-No real chance of incidental touching of metal parts (except when changing lamps and then power is off), so lack of ground is not really a concern.
-Newer lamps draw less current, so no fear of overloading wires.
-Do check the very ends for brittleness/work hardening. If possible, trim off 1/2 - 3/4" to get to clean wire(s).
-Not clear what you mean by "not the copper smaller wires". If by that you mean a single conductor and not a strand of many small wires, it's fine- typical. As long as the wires themselves are copper (just thicker insulation or whatever), then proceed as above.

If the wires are aluminum, then you really should bring in an electrician. Aluminum wiring was a cheaper alternative at one time, but age is not kind to aluminum and that could pose a threat to your entire house.