Very indoors, shut up tight, and at a suitable time of day.
If you live in a house (as opposed to a flat), and it has reasonably good insulation and tight-fitting windows, the high-pitched sound of a whistle will be significantly attenuated. The noise level is comparable to a burglar/car alarm siren, and they're fairly common. If you've ever heard an inside siren (only) going off from outside you'll get an idea of the attenuation.
Then if possible find a room or closet with no outside walls or windows, go in and shut the door. I'd use my downstairs cloakroom or even the cupboard under the stairs (the former has an extractor vent to outside which I know let's sound in). In such a confined space it's even more important to wear ear protection. Then a quick blow should be enough. I suggest rinsing it out in a cup of water and testing again while you're there, to ensure it works in the wet.
If your house a shares a wall with neighbours, try to do it while they're out. By this point, people in their own homes will barely notice, and it shouldn't be annoying to people outside, except right outside your house. You should still aim for a time when you won't disturb people - in the middle of the day presumably
If you're still worried, wait for lots of background noise - perhaps when the neighbours are cutting their grass. This will mask the sound as their nose is emitted outside, will make it less annoying as you're adding little to an existing noise, and will make the location of the source almost impossible to detect (a short blast remember).