Temporarily ignoring all the other issues and proposals...
To get some intuition on what frequencies will and won't work, we can look at some helpful charts from places
like this.
It doesn't actually go up to the correct frequency (we'll see why) but it provides simple equations we can evaluate ourselves.
If the transmitter works in air to about 90ft/27m, we can estimate the minimum detectable signal strength in dB, just assuming spherical emission -- it's about -29dB (the signal strength decreases as 1/distance^2 --> based on a reference position of 1m from transmitter the relative strength is 1^2/27^2 --> 10*log10(1^2/27^2) = -29 dB). For science-y reasons, spherical emission for this sort of device is a super good approximation.
Based on the webpage above, the attenuation at 400 MHz should be 0.0173*sqrt(frequency*conductivity)= 774 dB/m, assuming the worse stated conductivity value as a conservative bound (5 Siemens).
At 774 dB/m attenuation, you reach 29 dB of attenuation after only 3.75 cm.
Even if the exact conductivity values are substantially different in the water you're diving, it's unlikely you'll have the reliability you want.
It's likely you could have wireless transmission if you glued your fob to the exterior casing, but not if you want to hold it in your hand.
Going back to that plot in the link above, frequencies on the order of 100 kHz give you a few meters of propagation, you can get at least 1m propagation up to about 700 kHz. As
@Lorenzoid pointed out, this is probably why Shearwater uses that frequency band for its transmitters. If you want to go the wireless route, find something low frequency.