I have plenty of experience with the Perry plastic WotR sets, including some conversions, but I have not gone for a pike to spear conversion. I will say that their pike to halberd conversion IS a bit dodgy, as it is exactly what you describe: connecting the ends of two rods. While it will work with patience (you have to trim the ends to be at exactly complimentary angles, and ensure it's supported until the glue- proper plastic glue- fully dries), there are better ways:
My recommendation would be to cut the head of the pike off immediately at the base of the spearhead. Then remove the extra length of the pike shaft to make it a spear-length shaft. Then glue the spearhead back onto the shaft. This means that a) any tiny mis-alignment is less obvious than gluing shaft-to-shaft, and b) there is a much shorter glued-on bit sticking off, which means it is less likely to be bumped, and if it is, there is less torque applied to the glued join, so it's much less likely to break down the road.
I *do* have experience with drilling out the hands of the Perry plastics (to convert some of the Dismounted Man at Arms figures to hold wire pikes), and you can indeed drill out the hands easily enough… though the shouldered pike poses do not well lend themselves to removing the pike entirely for replacement with wire pike, because you don't just have to cut if from their hands, you have to cut it away from the clothes/ armor on the shoulder where it's molded touching. It can be done, but it takes way more effort than it's worth to do it without disfiguring the clothes/armor. I would recommend instead that you use the "cut-off-and-reattach-the-spearhead" technique I outlined above, and if you want extra strength, use a pin vise to drill a small pilot hole into the base of the spear tip you cut off the plastic pike, in order to make a stronger glue join between the shortened staff you cut down on the figure and the spear point.
Alternately, you can use the Bow and Bill box set, cut off the bills/halberds and drill out the hands for replacement with wire spears. Or do the same with some of the poses in the Dismounted Men at Arms box set, if you want very-well-armored spearmen/ Men at Arms with spear. The Bow and Bill poses are much more aggressive poses than the Mercenaries box, but they also probably work better for spear-and-shield.