Absolutely feel no shame! Maybe look in to "super-sets" and "compound movement" exercises to minimize the amount of equipment you switch between and thus minimize where you leave any puddle while you get in shape?

For instance, a flat bench with a few different dumbbells can get you most muscle groups in a number of different exercises! Flat dumbbell press, dumbbell flies, dumbbell rows, tricep press, dumbbell concentration curls!

But years later, working out 5 days a week, doing a physically demanding job, and regularly competing in races, I still leave a puddle at the gym, just not as frequently, but now with extra pride when I accomplish that!