When you want to express that you are taking precautions to ensure that everything goes well, you might say that you are "playing it safe" or "erring on the side of caution." Alternatively, you might say that you are "taking no chances" or "being careful." These phrases all convey a similar sentiment to the phrase "am on the safe side." Another way to put it is to say that you are "being prudent" or "mindful of potential risks." Whatever phrase you choose, the important thing is that you are taking steps to reduce the likelihood of problems so that you can achieve your desired outcome with confidence.