When we hit the other epistles there is not a great deal of mention of evangelism. Peter tells his recipients in the churches of Asia in 1 Pet 3:15 that they are to be prepared to answer the enquiries of unbelievers. This is what some call apologetic evangelism, responding to the questions of seekers. The sentiment is the same as Col 4:5-6 where the believer is to know how to answer the questions posed to them. This presupposes a readiness to preach the gospel when the opportunity arises (cf. Eph 6:15). That believers are the recipients of evangelism is found in references to those who came and preached to the recipients of Hebrews (Heb 4:2, 6; 1 Pet 1:25; 1 Jn 1:1-3). This suggests that the process will go on although this is not directly expressed.
Jude 23 is one of the clearest expressions of evangelism. Jude encourages his recipients to be merciful to those who doubt, those who are struggling in the faith. He then encourages believers to 'snatch others from the fire and save them' which is an expression encouraging evangelism. 'The fire' here is the 'punishment of eternal fire' referred to earlier in Jude 7. Thus believers are to be motivated to share the gospel in attitude, word and deed to the lost to seek to see them saved from the torment of eternal destruction.