I wouldn't take the Lagginhorn too lightly. What if the weather turns? What if there is snow on the ridge, or ice? It's still very high.
The only 4000er that I would possibly consider doing solo would be Breithorn, since the trail is so well trodden and you're never really alone up there. Bishorn is nice and very easy technically, but the Turtmann glacier has crevasses and the normal route goes parallel to them.
Guides aren't too expensive on the easy 4000ers (100-200 euros), and for a bit more you can also try something a little more exciting than a simple snow-trod, without having to worry too much.
If I were you, I would either go with a guide and do something fun if you really want the altitude, or just go for a little bit lower than 4000 meters, and just put in a bit more excercise at those altitudes (e.g. push-ups
)