You can certainly get into great shape with just bodyweight exercises. When I first started working out many years ago, I did a program that was mostly agility ladder work, DB work, and lots of pushups/burpees. My aerobic capacity was great and I got very lean but I was certainly not as muscular, explosive or powerful as I could have been if I took that same amount of time and focused on strength training. The problem is at some point your body will adapt and you will stop making progress. Dumbbells, especially for any form of deadlifts, are hard to load effectively and you will quickly need either heavier dbs or a barbell to load these properly as your strength will go up quickly.
You could probably take CT's look like a bodybuilder perform like an athlete program and substitute DB exercises using the same rep scheme and then supplement pullups/pushups but not sure how effective that would be because you will run into the same problem with needing heavier DB to progress at some point.
I would recommend you buy a weighted vest...you can get quite an upper body workout from just weighted pushups and weighted chins/pullups. If you have a back yard, sand bags, rocks, and other assorted heavy items might be option for loaded carries. Home gyms while convenient get expensive quick, if any gym becomes available I would use it. Good luck.