Home compounding is a good idea. You can mail order powdered salicylic acid -- it's about $15 for 8 ounces. SA is soluble in 191 proof EverClear, which costs about $8, and is sold in most states, but in some states it's not legal, so then you could buy 100% isopropanol from a chem lab supply store although it's more expensive than EverClear.
SA is not at all solvent in water, but it will remain dissolved and in suspension in a body wash, Dove Sensitive Skin for example. Keep the container sealed or the alcohol will slowly evaporate and the product will get a little bit too sticky.
To measure the SA, you can mail order a small scale, accurate to 0.1 gram, made by AWS for example, for about $30. Then you can buy a glass pipette that measures 1ml, which costs about $8, or you can buy a glass syringe that measures 5ml for about $8. The syringe is a little easier to use.
SA completely dissolves in alcohol at room temperature at a ratio of 1 part SA to 4 parts alcohol. If you want to make 100 ml of a 1% SA product, you would measure 1 gram of SA on the scale and pour it into a small glass container like a shot glass, and add 4ml of alcohol and stir, and then pour the dissolved SA into 100ml of whatever wash product you like. SA will make Dove body wash slightly thick, probably because the SA has a low pH and it reacts with the starch or the sodium chloride in the Dove, so you would start with 80ml of product, to leave room to add distilled water or more Dove to get a useable consistency.
Before you start, weigh the empty container, which will be an empty used-up shampoo bottle with a screw top, so you can then subtract the weight of the empty container from the weight on the scale, so you know how much Dove to start with in the container, then add the dissolved SA, and shake well.
When you make your own, you can start with 0.5% SA, in a small empty plastic bottle of about 150ml, and see if you like the results, and you could try a 1% SA but not more than 2%. I like 0.5% SA because it doesn't smell strongly -- even a 0.75% SA product smells too strong to be really useable in my opinion. You could skip the empty container and just make a very large batch in whatever original product you start with, but it is easier to make small batches when you are starting out, to see what you like.
I like 0.1% lemongrass oil in body wash, but tea tree oil is fine too, and you might like to try Manuka and Kanuke from New Zealand, as they are considered the "better" types of tea tree oil by some people, but you’ll have to experiment to see what percentage you like.