I have a blue CMYK color in my file and the file from the start was created with U.S. Web Coated (SWOP) v2 profile. Now when I know where I will print this work, of course I need to print it out with exact the same blue, but using profile ISO Coated v2 300% (ECI). When I switched in InDesign to this new profile, in swatches for this color the % numbers remained the same and the tone didn't changed on the screen. I haven't printed out a test yet but I wanted to ask, is it ok to do it in this way or when printing it out the tone for the color could change? It will be printed as proof and then glued on foam cardboard.
in swatches for this color the % numbers remained the same and the tone didn't changed on the screen.
That is how it is supposed to work. When you convert a document to another profile, you are not changing the colors in the document or how they appear. Color changes happen when you apply the wrong profile to a document, or use a document that doesn’t have a color profile.
If it looks the same to you on your screen, then I don't think you can get much closer. (I'm sure you have already calibrated your screen?) Wether your printer will print what it should, is a totally other issue. If it is good, it should - or at least be very close.
If I were you, I would just do a test. And provided you are really new to all this, then you should also test what it looks like, when you glue it to the cardboard. Glue, thin paper, color of cardboard etc. can have an impact on the final result.