The fact that you’ve made it impossible to roll an 8 by replacing 2d4 with 1d6+1 might impact the game just a bit. Also with 2d4 a 5 is 4x as likely (1+4, 2+3, 3+2, 4+1) as a 2 (1+1) or 8 (4+4); with 1d6+1 all outcomes from 2 to 7 are equally likely, so you’re far more likely to get a critical hit or critical miss (if the game has that sort of thing, and you adjust it for the reduced range).
The fact that you’ve made it impossible to roll an 8 by replacing 2d4 with 1d6+1 might impact the game just a bit. Also with 2d4 a 5 is 4x as likely (1+4, 2+3, 3+2, 4+1) as a 2 (1+1) or 8 (4+4); with 1d6+1 all outcomes from 2 to 7 are equally likely, so you’re far more likely to get a critical hit or critical miss (if the game has that sort of thing, and you adjust it for the reduced range).