Self-propelled? No, not a chance. It just sinks. If and when it detects that it has entered a liquid ocean, it detaches the sphere. Ideally, the remaining part will be only a bit more dense than neutrally buoyant so as to sink slowly once it hits water and give a bit of time before the remaining fiber runs out.
Surviving the pressure while maintaining reasonable internal volume and a low density is a challenge. Modern syntactic foams are pretty good, though–half the density of water and can survive the pressure at 10 km down on Earth. Europa has <15% the gravity and the pressure at depth is correspondingly lower.
It helps that only the instrument core needs to resist the pressure. The fiber unspooler can be somewhat exposed. The fiber itself has a volume of ~2/3 liter (assuming 250 µm diameter). I posit that it’s not an impossible challenge to build an unreeling system not too many times larger than that. A TOW missile does it and it unreels at 300 m/s. This probe unreels at 1 mm/s.
The first instrument–and one which might justify the mission all by itself–is a fiber speed indicator. The unit will sink through the ice at a fairly constant rate. That rate will change when it hits water or a rocky surface. We don’t know yet how thick the ice is and knowing just that would be very interesting. This can be a simple optical sensor that counts the number of loops that have unwound.
An accelerometer of some kind may prove useful. High accuracy probably isn’t very necessary since the probe doesn’t have hard contact with the surroundings; a tiny solid state unit should be accurate enough to give interesting data. Does the tidal flexing cause any seismic activity?
Similarly, a hydrophone to measure tidal activity. Flexing ice should make sound. It can be a flat transducer on the hull.
A thermometer loses much of its utility when connected to a giant heat source, but it’s tiny and it may be possible to use one to infer something about the surroundings. At the least, the equilibrium temperature will change between traveling through ice vs water, so it can act as a partial backup for the reel speed sensor.
A pressure sensor is probably redundant, but heck, science is about being surprised.
Salinity meter. A pH meter would be cool too, but might be too finicky for this application.
The remaining sensors need a view to the outside–probably using quartz windows. It may not be possible to fit all of them, but even one or two would be good.
A simple one would be a particulate meter. This could be as simple as measuring the scatter from a light beam. A fancier unit could use multiple frequencies, have a particle counter, or other measurements.
Somewhat more advanced would be a spectrometer. There are lots of choices here, and some are very small (including ones already in use on other probes).
Perhaps optimistically, a microscope. Fixed focus and magnification for simplicity. Probably only useful if there is some genuine possibility of the oceans teeming with life.
These are of course just some brainstorming ideas. Probably some of them are less interesting or less doable than they sound. But like I said, a probe that’s little more than a smart plumb bob would already give us information we don’t have right now, and convincingly select one of the handful of ice/ocean models.