Buy a stainless steel or brass safety razor and a pack of double-edge blades. Collect used blades in a tin and take them to metal recycling.
A disposable razor is about 10 g of plastic; one every two weeks is around 260 g a year, and none of it is recyclable because of the embedded blade. This is a classic eliminate-and-durable swap under the Ellen MacArthur Foundation's upstream-innovation framework.
The catch: there is a learning curve and a small cut risk in the first week; blades must be stored safely away from children.