So my 3ds really needed to be replaced so I decided to get a 2DS but there are some freeshop games that I want on the 2DS?Does it transfer?

Actually the content WILL be transferred, just the tickets won't. Tickets are what is required to make it show up in the home menu. To get the tickets back use tikShop. This will only give you the tickets from games available on freeShop, if you have any others you'll need to back up the tickets before the transfer and restore them after the transfer using FBI

If they haven't done it yet, I doubt they will. You'll have the same risk even if you only install one pirated game.tikShop gives the user tickets to everything on the eShop. EVERYTHING. Plus, there's the offside chance that Nintendo could start to cross-reference tickets in a future update, which might lead to potential bans.
If you don't want the tickets to be installed on your system, download the content via CIAngel or freeShop.
On the off-chance that you do decide to use tikShop or just want all of those tickets removed, use tikSweep: https://github.com/DanTheMan827/tikSweep/releases