If you can estimate speaker power, it probably is reasonable to use the ordinary power formula P = I²R for estimating the current the relay needs to handle. Typically, high-power speakers of a given kind are bigger than low-power speakers of the same kind. But as you can see from pictures of
40W speakers, some 10W speakers are smaller than some 5W speakers, and some are bigger than 40W speakers, so power estimation based on speaker size can be difficult.
If you have access to the sound source (tuner or player or whatever, connected to an amplifier) you may find output power listed on the amplifier.
In any case, due to the I² term in the power formula, the range of current to plan for is relatively small. For example, if 5W is going to an 8Ω speaker, 5/8 = I², and I = 0.79 A. If it's 40W, then I = 2.24 A. This range is likely to be handled ok by relays sold for ordinary use with Arduino systems.
Note 1: A relay's current rating ordinarily is derated significantly when the relay is used to switch DC or high-voltage AC. Audio is low-voltage AC and relay derating probably isn't needed. Note 2: The current a relay can safely switch in a live circuit may be much less than the unswitched current that closed contacts can carry. This might not be a problem with low-voltage audio. Note 3: Some commercial high-wattage audio distribution systems operate at higher voltages (see, eg, wikipedia's high-voltage audio distribution systems article, re 70.7 V etc systems); if you have one of those – as amplifier labeling might reveal – the example calculations shown above would need adapting.