Disclaimer: You asked my opinion, and this is just an opinion, worth exactly how much you paid for it.
Yes and no on Red Dot in 45 Colt. If you could find official data for cowboy loads using Red Dot in 45 Colt, then I would say yes. Unfortunately, there is not much official data for Red Dot in 45 Colt. No, I do not recommend wild catting unless you have many years of experience reloading.
Red Dot is made by Alliant. If you go to their website you can enter their on line reloading guide.
http://www.alliantpowder.com/reloaders/default.aspx
Alliant's data for Cowboy Action loads only lists three loads for 45 Colt, all using a 230 grain bullet. Bullseye, American Select, and Unique are the only powders listed, and frankly I think their charges are a little bit on the high side. I just searched my manuals, and I only found two recipes for Red Dot in 45 Colt in my well thumbed Lyman Pistol and Revolver Reloading Handbook, 2nd edition. No, I am not going to tell you what they are, you should look them up for yourself. Never trust data you get from an unofficial source over the internet, you never know what typos may be included.
With Alliant products I would have no problem with any starting loads published for Unique in 45 Colt. There is lots of data available on Unique.
Hodgdon (the maker of Trailboss) has a much better on line data website.
https://www.hodgdon.com/basic-manual-inquiry.html
You simply choose what type of round you want; pistol, rifle , or shotgun, then select the cartridge. You can select the bullet weight too. I would stick with 200, 215, and 225 grain bullets for cowboy loads. The beauty of the Hodgdon site is it gives you both pressure and velocity for starting loads as well as max loads. Check out Trailboss starting loads. I would be comfortable with anything down around 8000 psi in a Remington with a conversion cylinder. Remember what I said some time ago. Velocity alone tells you nothing about how safe a particular load may be for a particular firearm. Pressure is the important thing to bear in mind to be safe.
P.S. Reading between the lines now. I suspect you like Red Dot because that is what you have available. In better times when powder was more available than it is now, I always recommended not trying to make the one or two powders you like fit all purposes. Use the right powder for the right purpose. I would not hesitate to put starting loads of Unique or Trailboss in a Remington 1858 fitted with a conversion cylinder. At some point in the past I put some of my own light Unique loads through one of my Remingtons. No, I am not going to tell you the load, data is easily available. See if you can find some Unique or Trailboss.