I have an RCA 46" TV P46725SK into which I am installing the Tritronics
CTC-169 common failure repair kit.

My first step is to replace the HV splitter block. To do so, the small
HV splitter piggyback board must be swapped from the old block to the
new one. It's connected to the block by red & black leads which are
wire-wrapped to the board. Question: is it absolutely necessary to
wire-wrap the red & black leads to the piggyback board, or is it okay
to solder them on?

replace the HV splitter block
is it okay to solder them on?

It is ok to solder them on. It is very important if you solder to the
pins to go ahead and resolder the pins to the pcb as the heat from
soldering the wires may cause a cracked solder connection to the pins.

Do not forget to remove the old rubber ring insulators out of the old
block and place them on the wires. Do trim and tin (if needed) the
burnt lead and make sure ALL the solder flux is cleaned off the
re-dressed lead.

Get a tube of the spark plug wire clear silicone gel lubricant. Apply
a very small amount of the gel to the old rubber insulators for easier
insertion into the new hv block.

Update - installed the CTC-169 kit today and the TV is working again.
Beautiful... thanks to all for your help & expertise.