switched socket and unswitched light fixture to switched light fixture and unswitched outlet
First you will need to find out if the switched outlet circuit is powered at the switch or at the outlet. Then you will know whether to run your surface conduit from the light to the switch or from the light to the outlet.

You should also find where the light power cable originates. In an older home the light may be powered from the same place as the switched outlet. In that case you may not need the surface conduit.

Be aware that most electricians nowadays think it is a good idea to put the outlets in a house on 20A branches and the lights on 15A branches. If your house is wired this way, moving so many lights onto the outlet branches will obliterate the original electrician's load calculations.