Can I transfer an old ssd with windows on it to a new computer that already has an ssd with windows?

So I'm building my first computer soon and I'm planning on transferring my old drives (an ssd and hdd) over to my new build so I don't need to redownload most of my games or software. What I'm wondering is if I use a new ssd as the primary drive and install windows on it, will I have any issues plugging in my old ssd as a secondary that also has windows installed? And is there a way to delete windows from the old drive but keep all my downloads?