Sentence 2 is the better sentence; even though there will be several
signatures from the government, each company is applying for only one
signature.
You could also say, to be perfectly clear:
(a)
|
A/ Any/ Each/ Every company doing e-commerce should apply for
an/ its electronic signature from the government.
|
Or, to focus on the plural, you could say:
(b)
|
Companies doing e-commerce should apply for their electronic
signatures from the government.
|
Adding the possessive adjective their to sentence
(b) clarifies it.
These sentences could also be arranged with the phrase to the
government coming right after apply.
A company doing e-commerce should apply to the government for an
electronic signature.
Companies doing e-commerce should apply to the government for their
electronic signatures.