I don’t think the solar panel in your link would work to power the SCK alone, nor charge the battery enough to make it worth it.
The LiPo battery supplied with the kit puts out 3.7v. If you removed it and substituted the solar panel in your link, you would be under-powering the SCK.
I also don’t think it would make for a good alternative for the current solar panel. The current unit’s specs are 17 volts, 10 watts, 0.58 amps, which is stepped down and converted by the on-board components to fully charge the LiPo battery every day.
If you end up trying it, please post your results. I’d love to see the what you find.