I think the first reference in the literature for the result you want is Wen-Tsun Wu, On the isotopy of $C^r$-manifolds of dimension $n$ in Euclidean $(2n+1)$-space. Sci. Record (N.S.) 2 1958 271--275.

In it he proves any two $C^r$-embeddings $M^n \to \mathbb R^{2n+1}$ are isotopic, provided $n>1$. $M^n$ is any compact $n$-manifold. The techniques are now standard -- your two embeddings $f_0, f_1 : M \to \mathbb R^{2n+1}$ are homotopic $f_t : M \to \mathbb R^{2n+1}$ so you look at the "graph", $(x,t) \longmapsto (f_t(x), t)$ as a map $M \times [0,1] \to \mathbb R^{2n+!} \times [0,1]$ and then approximate by an immersion and consider appropriate usage of the Whitney trick.

I think the first reference in the literature for the result you want is Wen-Tsun Wu, On the isotopy of $C^r$-manifolds of dimension $n$ in Euclidean $(2n+1)$-space. Sci. Record (N.S.) 2 1958 271--275.

In it he proves any two $C^r$-embeddings $M^n \to \mathbb R^{2n+1}$ are isotopic, provided $n>1$. $M^n$ is any compact $n$-manifold (the title does not mention he also assumed connected, but it is). The techniques are now standard -- your two embeddings $f_0, f_1 : M \to \mathbb R^{2n+1}$ are homotopic $f_t : M \to \mathbb R^{2n+1}$ so you look at the "graph", $(x,t) \longmapsto (f_t(x), t)$ as a map $M \times [0,1] \to \mathbb R^{2n+!} \times [0,1]$ and then approximate by an immersion and consider appropriate usage of the Whitney trick.