Are there low-fat substitutes for shortening in baking?
what you are looking for does not exist. 


  a way to make the food [low fat] for him without losing flavor 


This is impossible. Fat is very important in baking for both taste and texture. Assuming that your husband's fat/salt/sugar diet means that the substitute has to contain less fat per unit of weight than shortening, you will be losing lots of flavor and texture. There is no way around it. 
The next best thing is to continue baking, but use recipes designed with low fat and sugar content in mind. Altering recipes is a very hard thing to do in general, especially when you are removing a major ingredient. 
If you are determined to try altering, here some general advice: 


Some baked goods depend a lot on (solid) fat. You will not be able to make any of them in a fat-reduced version. These include pie crust, Danish, millefeuille, and other pastry doughs. They can be made with butter or coconut fat or lard in the same amounts, but the result will have just as much fat. 
Batter-based baked goods can be made with reduced fat. The taste and texture will suffer, and also the shelf life (they will dry out earlier). It is especially tricky if you are reducing the sugar at the same time. You will never have the same quality as with a normal recipe, but most people find fat- and sugar-reduced recipes good enough for their taste. You need something to make up for the bulk lost, but also hold moisture and provide taste. Typical substitutes are fruit purees (especially from high-pectin fruits), dairy products (e.g. sour cream) and, if you feel adventurous, emulsions with a little fat, a lot of flavorful liquid and an emulsifier such as xanthan. 


This type of substitution works for cakes and quick breads leavened with baking powder. You can use baking soda, but will have to adjust for the new acidity levels if you are using fruit purees or fermented dairy. Other leavening methods will be much harder to get to work. Especially the bisquits (in the Southern US meaning of the word) will probably be impossible to make without a solid fat. 


Yeast doughs don't need a substitute. Just leave as much fat out as you want to. The texture will change drastically towards plain bread, but there is no way around it. 
Cookies are a problematic topic. Many of them need both fat and sugar. Some types can work with less, but getting these to work and finding a proper substitute will be very hard. It is easier to search around for new recipes; the chance that you can alter the ones you already have to get satisfying results is very, very low.  See also:  What are some low fat butter substitutes for cookies?