Are there any denominations that do NOT practice "laying on of hands" with the specific goal of having a new believer receive the Holy Ghost?

Jehovah’s Witnesses acknowledge that in Hebrews 6:2 Paul was likely referring to the laying on of hands to transmit gifts of the spirit to new believers. https://wol.jw.org/en/wol/d/r1/lp-e/2008688 However, they do not practice the “laying on of hands” so that a new believer might receive the Holy Ghost at baptism.

First, it is necessary to realise that the Holy Ghost, or the Holy Spirit, is viewed as Jehovah’s active force or energy, sometimes likened to electricity or wind. They only ever refer to it as ‘holy spirit’.

A person who is baptized “in the name of” the holy spirit recognizes the power and role of the holy spirit in accomplishing God’s will. https://www.jw.org/en/bible-teachings/questions/what-is-the-holy-spirit/

Second, they believe that only 144,000 persons since the time of Jesus can ever be “anointed” with Jehovah’s spirit. To be “anointed” means they have been given a heavenly hope and they will be co-rulers with Christ Jesus in his heavenly kingdom. Nobody lays hands on any Jehovah’s Witness who professes to have been “anointed” – they simply experience the holy spirit and then partake of the bread and wine at the annual memorial of the death of Jesus. This is how others realise they are part of the spirit-filled, anointed remnant of the 144,000 who have a heavenly calling. Here is a brief extract from an article about baptism, being born again and the holy spirit:

Jesus was the first person to be born again. He was baptized in the Jordan River, after which God anointed (or, baptized) him with holy spirit. Jesus was thus born again by holy spirit as a son of God with the hope of returning to life in heaven. (Mark 1:9-11) God fulfilled this hope by resurrecting Jesus as a spirit creature.—Acts 13:33. Others who are born again are also baptized in water before they receive the holy spirit. * (Acts 2:38, 41) They then have the sure hope of life in heaven, which God will fulfill in the resurrection... God chooses those who will be born again, or anointed with holy spirit. According to the Bible, being born again “depends, not on a person’s desire or on his effort, but on God.” (Romans 9:16) The expression “born again” can also be rendered “born from above,” confirming that the selection of those who are born again comes “from above,” or from God. Source: https://www.jw.org/en/bible-teachings/questions/what-does-it-mean-to-be-born-again/

Third, the majority of Jehovah’s Witnesses only expect to receive “a portion” of Jehovah’s spirit. They will not be “anointed” because they have an earthly hope and will not be part of the ruling, heavenly 144,000 class. When a person decides to dedicate their life to Jehovah and his earthly organisation, they submit to water baptism by full immersion. They do not expect to receive the Holy Ghost or the Holy Spirit as a result – but they have been told they can expect to receive Jehovah’s blessing and be empowered by his spirit as long as they remain faithful, obedient and loyal to his organisation. The 2016 Study Watchtower article ‘The Spirit Bears Witness with Our Spirit’ says that not all anointed Christians receive their anointing at their baptism then speaks about those who are not part of the 144,000 and who do not want to go to heaven:

15 Jehovah’s spirit works with equal force in those who have the hope of living forever on earth. In fact, if you are wondering whether you have received the heavenly calling, that would in itself indicate that you have not received it. Those called by Jehovah do not wonder whether they have been invited or not! They know!

17 The vast majority of God’s servants today do not have this heavenly calling. They entertain the same hope as did David, John the Baptist, and other faithful men and women of old. Like Abraham, they look forward to living as subjects under the Kingdom arrangement. (Heb. 11:10) Only a remnant of those selected for heavenly life remains here on earth in this time of the end. (Rev. 12:17) This means that the majority of the 144,000 chosen ones have already died faithfully. Source: https://wol.jw.org/en/wol/d/r1/lp-e/2016045?q=Anointing&p=par

To receive the help of holy spirit, we must pray for it with persistence.... holy spirit helps us in two ways. First, it gives us the power we need to overcome trials. Second, it is the force that “fills our sails,” helping us to move forward in serving Jehovah with life in God’s new world in view. Source: Watchtower November 2019 Study Edition Article: https://www.jw.org/en/library/magazines/watchtower-study-november-2019/how-holy-spirit-helps-us/

Finally, there are no “manifestations” other than an inward conviction that they have been chosen by Jehovah to be co-rulers with Christ in his heavenly kingdom and a zeal to remain faithful until the end.

I leave you with a link to a 2016 Watchtower Study article which goes into greater detail about how they view being anointed and experiencing the new birth:
https://wol.jw.org/en/wol/d/r1/lp-e/2016045?q=Anointing&p=par

For Baptists, Anabaptists and related denominations the only time where any kind of "process" is observed for new converts is at baptism. At none of these churches have I ever seen "laying on of hands" done as part of baptism. Laying on of hands is more often used in the commissioning of a believer to a particular mission or office.