I certainly won't stop you from using key limes in your pie if you want, but I want to assure you that they are not necessary.
I'm a chef, and I've made key lime pie with both key limes and what we know in the U.S. as "persian limes," the larger ones. Most people I know either cannot tell the difference, or they prefer the one made with the larger limes. Should you use key limes, you will have a lot of work juicing those tiny limes (key limes are about 1" to 1.25" in diameter), and you will need about 15 to 20 of them for this recipe.
Allow me to share my recipe with you. It's very good.
4 teaspoons grated lime zest
1/2 cup lime juice from 3 to 4 limes
4 large egg yolks
1 (14-ounce) can sweetened condensed milk
Graham Cracker Crust
11 graham crackers , processed to fine crumbs (1 1/4 cups)
3 tablespoons granulated sugar
5 tablespoons unsalted butter , melted
Whipped Cream Topping
3/4 cup heavy cream
1/4 cup confectioners' sugar
1/2 lime , sliced paper thin and dipped in sugar (optional)
For the Filling: Whisk zest and yolks in medium bowl until tinted light green, about 2 minutes. Beat in milk, then juice; set aside at room temperature to thicken.
For the Crust: Adjust oven rack to center position and heat oven to 325 degrees. Mix crumbs and sugar in medium bowl. Add butter; stir with fork until well blended. Pour mixture into 9-inch pie pan; press crumbs over bottom and up sides of pan to form even crust. Bake until lightly browned and fragrant, about 15 minutes. Transfer pan to wire rack; cool to room temperature, about 20 minutes.
Pour lime filling into crust; bake until center is set, yet wiggly when jiggled, 15 to 17 minutes. Return pie to wire rack; cool to room temperature. Refrigerate until well chilled, at least 3 hours. (Can be covered with lightly oiled or oil-sprayed plastic wrap laid directly on filling and refrigerated up to 1 day.)
For the Whipped Cream: Up to 2 hours before serving, whip cream in medium bowl to very soft peaks. Adding confectioners’ sugar 1 tablespoon at a time, continue whipping to just-stiff peaks. Decoratively pipe whipped cream over filling or spread evenly with rubber spatula. Garnish with optional sugared lime slices and serve.
Some suggestions and tips: In the U.S., one cup = 240 ml, so 3/4 cup is 180 ml. A tablespoon is 15 ml. Instead of graham crackers, if you can't obtain them, use any bland biscuit. Powdered sugar is icing sugar. If you prefer, you can use a meringue atop the pie, rather than whipped cream, although the whipped cream is more traditional. Some recipes don't have you bake the filling, but I think baking improves the texture by firming it just enough--otherwise, the filling in KLP is often runny.