I'm a native English speaker originally from Canada currently living in the US.
YES, it is perfectly acceptable for you to say "I play a little piano." with the intended meaning that you are not a very skilled player. As explained below, it might help if you emphasize the word "little".
Some more details...
The phrase is somewhat ambiguous, as it may mean either that you are not very skilled or that you do not play very frequently. If you are in the unusual situation that you play lots of piano but are still very bad at it, you might want to consider an alternative phrase: Maybe, "I play piano, but I'm not very good."
It will not be misinterpreted as you misspeaking and claiming that you play a small-sized piano, except that -- because that is a technically possible meaning of the phrase -- someone might make a (terrible) joke: "Yes, I play a little piano." "Do you have a tiny bench, too?" "Ha, ha, ha! I see you made a little joke there." See the "I play a little guitar" meme for another example.
Here are a few random examples in bios, interviews, or blogs of people using the phase with the intended meaning that they don't consider themselves very skilled: "I play a little piano...I have a long way to go" and "I play a little piano and drums but certainly not well enough that I would ever consider playing them live.". Here are some examples of people using the phrase with the probable intended meaning that they don't play very often, usually set in contrast to some other activity: "I play a little piano, but I mainly sing." or "I play a little piano, but mostly guitar"
As someone mentioned in a comment, it is the sort of phrase that may used by someone who is very skilled or plays very often, but is either being modest or ironic. For example, Magnus Carlsen is a very skilled and famous chess player. If someone were to ask if he plays board games, he might jokingly say "Yeah, I play a little chess." Or see "I guess I play a little chess" from an amateur who has played many games.
As noted above, emphasizing the word "little" is likely to make it clear that you are not being modest. It also may indicate that you are talking about skill rather than frequency. If you say "I play a little piano" or "I speak a little English", it will probably be interpreted to mean that you are honestly claiming your skill is limited. Unfortunately, I couldn't find a reference to support this claim. Maybe someone else can find one.
Note that the meaning may be different for other activities, even when "little" is emphasized. If you say "I do a little exercise" or "I watch a little TV", you are more likely to be commenting on frequency rather than personal skill.