I would avoid the 1B label for as long as you can. I'm sure better coaches will decide for themselves and not care all that much about labels, but I don't think its worth the risk. For many it comes across as "I'm not good enough or quick enough to play anywhere else." I'd let a coach tell ME that I'm now a 1B versus telling the coach that I am.
Just like every other sport, the game is getting faster and faster. Gone are the days of someone like Ortiz playing 1B. The talent pool is so deep in college ball right now that many coaches are staffing 1B with guys who were all-state SS's in HS. A school my son is targeting in the AAC has exactly that right now. A local D1 here from the Summit league had 3-4 guys play 1B at some point this season. All were OF's previously.
My son is playing Juco ball (started this week) in the Kansas Jayhawk conference and his HC told me he doesn't recruit 1B. His exact words were "why would I want anyone who can only do one thing?" Cast the widest net you can for as long as you can. If 1B is his ultimate destination, he can get touches at other positions that will get him awfully close to being ready to play 1B should that time come. But I'd encourage anyone who may end up at 1B to get as many reps picking balls as they can on their own. In my mind, the ability to scoop is THE thing that separates good 1B from great ones. Full disclosure - this is coming from the dad of a SS who doesn't always hit his 1B in the chest. The scoop is often a necessary partner in an outstanding play. Without it, they often call it an E6.