It'll work as a siege missile or PDC crackers. They won't be able to catch moving ships for crap, at least not beyond fairly low tech aliens. Though 20 MSP is pretty noticible compared to size 6.
Then I guess that I can drop the warhead power, again. Man, designing anti-ship missiles are hard at the lower tech levels. What should I be aiming for, stats-wise? More speed? More maneuverability?
It's really, really not. Up until ~TL5-6 you can get by with WH4, being the first square above WH1. There's a balance to be struck between drive and agility that will maximize CTH; it's more difficult to find without Paul's missile design spreadsheet, but you can usually figure it out with a minute or two of effort. Slightly more difficult now that you need to design missile drives rather than just putting points into it, though. For your tech, 20k km/s would be a reasonable velocity, and whatever amount of points in agility maximizes CTH. For range, around 60-80m km is again reasonable for your tech level. Aim for a size-4 or size-5 missile, and put whatever spare partial points are left into an active sensor.
The design challenge has always been about balancing drive and agility for the best possible combination of CTH and velocity; it's shifted a bit in the direction of coming up with a near-ideal balance of drive efficiency and power, but as before WH and fuel are largely known variables that won't change very much.
Start with your STR-4 WH, come up with a good drive design, put in whatever agility you need to maximize CTH, give it enough fuel to hit that 60-80m km range (or as close as possible[for your tech, at least]), and then slip the leftovers into a sensor.