Using No Insecticides
Early Warning Trick
The moth or adult of the squash vine borer is attracted to the color yellow, according to the Mother Earth News. They suggest setting out a yellow pan of water among the plants. Moths will be found floating in the water, alerting you to their presence so you can begin to take preventive action. There is no reason yellow sticky traps would not work the same way. Go to Yardener's Tool Shed for Yellow Sticky Trap Products.
Using Natural Insect Repellents
There are several natural insect repellents that often kill the moth of the Squash Vine Borer on contact, but also serves as a repellent by creating a bad taste for the critter and make it go someplace else to munch and lay eggs. Neem Oil Soap, Hot Pepper Wax, and Garlic Barrier all have this potential repellent capability when applied properly on the tops and the bottoms of leaves of the target plant at least two weeks before you expect the Moth to arrive, probably around the first of May. The repelling effect will last for several weeks to a month depending on the weather conditions, so you may wish to add another application every two weeks or so. See the Natural Repellents in Yardener's Tool Shed.
Try Bt Injections
Once the borer is inside the stem they can be controlled by injecting the squash vine with Bacillus thuriengensis (BT). You can use a disposable hypodermic needle from the pharmacy (3-cc size will do) or even better a glue injector used in wood working. Timing is most important in using the injection method. Give plants their first inoculation just after the first flush of flowers appears. Shooting BT into the stems bathes the borers' food supply with bacteria. Infecting them just after they hatch prevents borers from doing much damage to the inside of the stem. Inject the plants again in a week to 10 days. The liquid form of BT works best. Mix it in normal solution just before you're ready to use it. Gardeners also recommend preparing a bowl of disinfectant such as chlorine bleach mixed with an equal amount of water, and using that solution and clean water to clean and rinse the syringe between injections. Cleaning the syringe between injections reduces the possibility of spreading disease from one plant to another. Stick the needle right into the center of the stem, about 1;1/2 inches above the soil line. This is approximately where the borers will feed first after hatching. The idea is to wash the hollow interior of the stem with BT so that the tiny borers eat it as they feed. Use about 1 cc of BT per injection. (If you inject too much, it will flow back out of the stem through the hole made by the needle.) It's fine to stick the needle into the holes left by borers that have already entered the stem, though the borers tend to move slowly upward as they feed. In advanced cases of infestation, it may be more effective to make the injection about an inch above the borer holes.