There is only one sort of moving Den Den Mushi.
The only place where you see then is in the Tenth movie
Self-Propelled Visual Den Den Mushi
Shiki has a variant of the Visual Den Den Mushi called the
Self-Propelled Visual Den Den Mushi (自走式映像転送電伝虫 Jisō-shiki Eizō Tensō
Den-den Mushi?). As the name implies they are able to move and look
around. They also appear to be close to the same size as the larger
variant of the Visual Den Den Mushi and have attachments that allow
them to project what they can see to a monitor.
The Den Den mushi are normal snails untill people attach the phones to them.
This is taken from SBS 41(Q&A with author)
D: In Chapter 367, Sanji-kun destroys the Den Den Mushi. That's so
mean!!! The Den Den Mushi didn't do anything wrong! Even a Den Den
Mushi would cry if that happened to it! It cries when it hurts! It
cries because its heart hurts even more than its body! So let's
apologize to it, shall we? P.N. Naoko
O: Oh, well, you see... OK, I
admit, I may have created that impression, but it's okay. On the right
is a wild Den Den Mushi. It has the ability to communicate with its
species through radio (thought) waves. Humans attach buttons and
receivers to them so they can contact specific other Den Den Mushi.
So, you can destroy the receiver without hurting the Den Den Mushi.